It's been on my wish list for some time.
Glad to hear that.
I came across another "gem" book about the little known company that made the customs for P, et al "Creative Industries of Detroit." long defunct. Most of the fun is what you run into looking for what your looking for and don't find.

Definitely check it's turning. You can do that in the drive with some rear stands or on a lift. Not sure if cable will jump out of place disconnected and turning at road speed.
It's most likely in the "clock" mechanism that turns the needle/dials since it's intermittent and cable is good. Usually if the drive gear reduction is bad/stripped it won't work at all and I've never had one go on any of my >100K mi vehicles Some of those internal speedo gears/parts are usually plastic. Since it hadn't run in a while it's maybe seized a bit. There's usually a little grease on them which can harden. It's a 70 yr old piece like me, I don't work all the time anymore either... Might just need a good cleaning.
Frankly if it isn't making noise, I wouldn't worry about it. See if it starts again. You're way past odometer laws and a GPS will give your speed much more accurately. There's apps for that.
The speedo can probably be repaired but I don't know about getting Packard parts or who made their's. I send those parts out let others worry or replace.
The cables usually break from lack of lube and fatigue/wear. Used to be pretty common replacement items until digital dashes. So much so they came out with the "universal" cable which had its issues ala Ross.
I used to have a GM speedo cable luber from back in the day, but don't know what happened to it. I guess someone borrowed/lifted it from the old man's garage after I left. I haven't seen any since. Short lived invention. Then there's the graphite vs non arguments, but white lithium is OK by me. Don't need much. Maybe I should market "genuine synthetic" speedo cable lube?

or just buy one from Waldron's, et al.
I'd be curious to know how well it matches the OEM replacements from the computerized bending equipment and how they knew to make the muffler longer/or off the shelf/listed.
I bought one from the guy in NC in the PAC ads for the '49 and it fit like a glove and the xframes are tough to navigate pipes thru. It was very reasonable back then. I expect today, you have to bring the first born for the exchange at least an arm. I picked it up from his shop. I think he's since sold that business/don't keep up.
As the old saw goes, if you get a carpenter to fix something expect a few hammer blows, so goes it for industrial designers and mock ups. To each his own according to their abilities in DIY land.
When it said "modeling" I was expecting something different than a .pdf like 3D sketch or something. Not many homes have a laser scanner to generate the mesh. I don't even have AutoCaD any more since I re-retired. Everything is pay by the month now even Adobe. At zero usage that's infinite cost/month. I liked the pay for it once era. It makes us retirees take the free offer then cancel with we need something. They're getting tricky, and send you a pop-up and if you touch the screen it bills you. Happened again today. ottabalawaginit.

There's two problems pressure and delivery/flowrate when you install an electric pump on a formerly mechanical. Most of what's out there is made for FI and is too high pressure and recycles the excess flow to the gas tank w/ or w/o a regulator. Some are internally/self regulated.
It's probably obvious that yours has too much pressure, if it ruptured the mechanical's diaphragm or leaks out the housing. There is one I used(12VDC) that's made for carb cars that has the right pressure and flow. I'm not aware of 6Vs. It's a bit noisy but works in a full replacement where mechanical is bypassed. It's also wise to go the extra mile and do the electrical upgrade(relays,breaker, and multi-pole pressure switch) to avoid the pump running when it shouldn't. Not enough amperage to run off the ignition.
That info will come with the pump usually and there's a few good online help. Just putting on a manual switch is dangerous.

One has to watch how they work on old chrome, as if not right, you'll haze or scratch. Especially if you incorrectly used a buffing wheel. Almost impossible to remove haze causing by improper buffing. Always best like dealing with old paint to start low and get more aggressive as needed.
Since it's 3 layers, you have to assess what the issue is. Iron/rust stains are the base metal coming through so that means the three layers are damaged/porous. Vertigris/green stuff is the base copper oxides.
Pitting is not going to come off - they go all the way to the base metal. About all you hope to do is flatten it as best one can but that requires the edges to flake off and leaves a "sore".
If it's dull, then most likely the chrome has worn off from years of "polishing" and the underlying nickel is showing.
We've had all sorts of "home" remedies/stories since they started putting lots of chrome on cars. CocaCola and crumpled aluminum foil was big post war. I don't fall for these, nor agree with some of what's been said above...aka;hearsay.
The best thing I found, which is no longer available, is Simoniz chrome cleaner. I still have a part can that I hoard for special occasions, but nearly exhausted.
I wish there was a magic or easy method, but experience goes a long way on what to expect. Elbow grease is the other part. We learned as kids collecting what are now vintage hub caps off the side of the road/trash and cleaning them up. About the best case is when the remaining good can be polished bright to out shine the bad, aka; driver quality.
By all means, wax it once it's shiny. Most all the carnauba waxes will do, harder is better, but need to be removed and reapplied regularly. I've successfully used Nu Finish on chrome, but it's a drying to powder material and careful to apply and requires detailing to get the white stuff off, it'll go into pits. It lasts a year or so. You'll find many a car with lots of paste residue under the chrome which holds moisture. These new fangled silicon polishes are very hydrophobic but don't live up to their reputation on life expectancy over cost, in my experience. They also require re-application and are harder to remove.
ps: from the window sticker, the cost to re-chrome all that is multiples of what you paid for it. I spent that much just on the trim, a decade ago. I just went through and still succumbing to Biden sticker shock on a few pieces I sent out last month.

almost impossible to determine without knowing when and by whom the re-paint was done. Fading, etc. will change the pigments over time.
If it was a factory "gold car", then it's a rare bird - 50th anniversary car. 1 of ~400.
If you want to match or paint something 23 series period the paint charts are on this site and/or TCP Global "autocolorlibrary.com" archive. They can match some of the paint colors.

ps: Uncle Earl is still in business at some franchise locations I thought? He's long passed on and the business went out in 2010.

Speculation doesn't help without talking to the owner/listing, etc. Without popping the hood, trunk, etc. and vehicle history just this picture is undistinguishable.
I would guess you'd have to check the Henney literature and see if A/C was an option in '53.
Parts lists, pictures, etc. may show some fixtures. Most of the big cars had two units, front and rear.

I think with manual trans, not engaging the hand brake has serious consequence when parked on a grade, hill, slope, etc. Some sort of "alarm" that it's "on" would be of use. Just watch any 3 stooges short and it'll be clear.
Once, I was parked at a gas station @ 4 AM waiting for tourney partner to arrive. I had my manual trans P/U truck and boat. I had my E-brake on, but apparently not fully and motor off and I was went in the boat arranging/setting up. Would U believe while I was in the boat for a few minutes someone pulled in and parked in front of and in line to me and opened their hatch. The truck started to roll on its own for no reason. I guess it was the gravitational attraction between the two vehicles? I yelled and the other guy got out the way but before I could jump down and jump in cab to hit the brakes, my rig rolled into the other vehicle. I always leave my door open now when I'm out of the truck for fast entry and more judiciously pick my parking spots. A few years ago there was a video of a luxury motorhome and guy launching his boat. While he's in the boat, the motorhome rolls into the lake. Dog was inside and suspect. Sometimes the deck is stacked against by mysterious forces.

We've kicked the tires on this before. I've never been convinced this is worth the effort. The max. boost is determined by the flat head pressure rating, which isn't stellar as a flat piece of iron, so even if it can hold 15-20 psig without gasket blowing, that's not much HP. Plus one needs to enhance the spark system for igniting pressure charges. Yes, ~twice HP what was stock(circa 130), but still way low to current stds. <<300. HP/wt ratio still sucks as very heavy engine blocks. Of course, hot rodding is/was more about cool factor in some respects. I'd choose a turbo as it's not parasitic and can vent boost. There's several of those around or pictures of same. The supercharger typically has fuel mixed in and spins relative to the rpm, so care has to be taken to not scatter things at WOT. Much like a run-away condition can occur. Typical at the drag strip to see a blower explosion back in the day and why they came up with the fragment jackets/blankets. Now with computers and new materials, it's a better HP world. One can take a LS block and make 1000 HP for less than $10K these days. I wouldn't even ride in some of these rat rods. They're not safe. Cool maybe, safe not most.

What have you done to diagnose it as a stuck valve? Or just assuming?
Noise can be a few things. Zero compression can also.
The side adjustment cover comes off and you can look at the valves/tappets.
Without knowing any info on the vehicle, it's near impossible to diagnose or offer solutions over the internet.
Some of these products can also cause issues with deposits. These engines don't have full filtration so the block may be crudded up and cause a lack of lubrication issue. Adding stuff to oil or gas can dislodge deposits and make things worse.
Do you crank without firing until the oil pressure comes up before starting to get oil to the cylinders or do you start it and rev to warm up? Former not the later is good practice.