The color charts '49,'50,'51 (23 & 24) are all the same should be on here. The PAC has them as well as other paints sites.
The one's I've seen are Ditzler (DuPont) lacquer and enamel. Probably won't be able to get factory paint these days. There have been several name changes since then and now Axalta.
Should be able to match, if formula exists.
I think the trunk matches exterior color.

The paint and trim codes should tell you what color/trim it was, but they weren't always punched and didn't survive. So without a build record, need paint forensics, if it wasn't taken to bare metal. A P restorer may help.

PAC has the color and trim info. Also, roster people, but I didn't find them particularly useful in this period.

I see a lot of work and alignment issues with that approach.
If they're weld nuts, see if any bolt sticks out the back you can get to, penetrant soak, and wiggle with the vice grips to loosen. At least get all the easy ones first.
Heat might also work, but need to be careful, use the brazing torch with a pencil point and only heat the center of the snapped off bolt. Bring to red heat then remove heat, don't go white. Repeat if needed, but give up after 2 shots.
I think drilling will be tedious, but maybe the last resort. Downside some of the threads can get damaged.
Could try the easy out, but if that corroded, may not work. I like the reverse twist drill bits, they sometimes come out on there own.
You could possibly flush grind (watching heat)or air stick grind the nut off the tab, then switch to "J" nuts or weld on a new one. I prefer to stick with what's original if at all possible.

Obviously there's a cure for it or would never have matched the other side.

One of those can't diagnose over the internet, have to open it up and look see what's "wrong". If not able, take to body shop. Door panel/handle removal required. I think these are "pin type" connected handles. Put lots of light on the subject and exercise the parts and see what's not acting, missing, worn, or bent.
Typical of wear/abuse, since the other side does not suffer the same fate. People/children tend to hang on door handles and slam things, so this is what happens. PO was possibly type "A". May have been misaligned/lack of lubrication at some point and hard to close, so more and more force was used. Rather than fix the problem, they tend to get angry with it and muscle until a "now look what you did" situation occurs.
May need to replace assy(s) or a guess is: the latch return spring is broken, missing, or worn. Torsional springs tend to lose tension more easily with use and would be typical, as noted.
Have no idea where you'd find a spring - may have to make. Unless similar to other brands.
No idea who made these parts for the body company? I don't know of any interchange here either, but early or later may adapt as P ran in "series" which span more than one model year.
The "usual" sources may have used parts(?)
Spray a little white lithium grease on the working parts when re-installed/done. Should be in the lube schedule. Of all the auto dealers I've dealt with, only one actually lubed the doors as std protocol. Nice touch, A+

I guess need to determine if the movement is a problem.
Does the door hit the striker when you close it or not? (ie, can it be adjusted out) Or only moves when you push down on it when open but goes back on it's own?
Conv/2drs are heavier and need more A pillar support.
Assuming it's not collison damage, rot, or loose fasteners, then probably worn pins, but what's the mileage, history -how stored, etc.? ie, does it match the overall condition. Usually driver's door gets more wear.
Pins/hinges can be removed and inspected/replaced. Just make sure you have some help with the door. Difficult to re-align without tools or extra man.
If it's a design issue as HH reports,(not loose, properly adjusted,not worn) then need to get the right/later fix. I would not weld the hinge on, but put a stiffener in behind.
Maybe one to take to the bodyman/shop depending on your capabilities.

The front bumper is one piece? The uprights/bumperettes, etc. are separate/bolt ons. Has several attaching brackets.

48-49 would be 22 series, which has the painted middle insert.
The 23 series '49 is unpainted but I think is the same part number.(? - have to look up) Just repaint the middle.

FYI; Would cost a small fortune to replate one of these. My plan was to slim down/light weight on my hot rod project, sitting under the bench...
Check the usual places.

ps: post on the "parts wanted" forum.

Simple economics. Can't save them all especially in this current environment. Even good plans/performance can fail due to outside factors, aka, risk.
I guess this guy bought with his $/ft2 eyes and not with a sense of reality. Isn't real estate credo, location, location, location?

Since it's a "left over" '49 1950, aka 23 series (23xx-5) the '49 - '51 paint charts apply and are the same/correct.
The photos color match to the paint charts* isn't good, like most pictures of "chips". Light when taken, etc., condition of both paints comes into play.
The two candidates given, are both "poly" or metallic flake, offered in enamel and lacquer, so there's a fair amount of variation in application. Flake should be observable in the finish for either.

My eyes, closest match is the 30469 Egyptian sand poly(lighter hue than argentine). But we're talking 70 year old paint, if original, so I'd expect variation/fading.
Without the paint code off the trim tag/build sheet, can not be conclusive. Can not even assume original paint without documentation and paint forensics.
One could buy some, ~1/2 pt, paint a sample and compare.
Test car with hand held colorimeter connected to the paint database.

* - Packinfo and auto color library same Ditzler charts.

Lots of debate on the proper lube for speedo cables.
I'd look in the service manual first. Then period Motors or similar auto manuals for documentation.
If it has an "oiler" and "felt wick" it's correct to suspect oil is proper as the speedoman sed.

I know the Cads don't recommend graphite, gets up in the "clock" and they used to sell a GM cable luber, I had one, that had white lithium grease in it. But that was later vintage well after Packard. Other's swear by graphite, so choose accordingly.
Petrified grommets are pretty common. I'd replace, as you want to seal out the engine vapors. CO is a silent killer.

That's the one pictured but the Neal narrative goes a little deeper about making that a 23 series model, 2373. Apparently, in preceeding pages, the decision to stake the wagon tool up was a bust. Not selling the "quota" to break even and many left over in '48. I would suspect some "scrambling" to sell that pile, but speculates.
From an aesthetic view, the wood looks kinda outta place, "pasted" on and doesn't really fit. "Sans door wood" looks much cleaner.
I'm in the camp that says this "hunk" is no rarebird. Just need more proof.

I assume you have a "problem" with it and not just out testing for the curiosity of it?
Not sure I understand how you're measuring, but I think you're not measuring full amps if using the "gauge" leads. That's not really an "ammeter". It measures relative direction of current flow. A coil creates a field as the current flows and the magnetic needle moves with the field polarity. More current stronger field, more deflection. When needles in the "center", it's supposedly fully charged up but can still be drawing low amps. I think you have to measure on the output lead. If you have a clamp type ammeter it's easier than putting DVM in series.
I recall that '49 gen is rated 30 or 35 A. So if pulling 20, not much left at idle. If you need more power, then ether change the gen or have rewound. I think there's an amp v rpm chart, in the shop manual, I seen it, not sure where. Maybe Delco?
Take to the local parts store that has diagnostic tools and let them put their battery machine on it. They can test 6V.
Or an auto electric shop and let them test it all. Some charge, some don't.
Another thing to do is have someone pedal the gas while parked in neutral and observe the lights from the side (safety) They should not go dim at idle. A small difference is ok. I'd suspect the battery if dimming alot.