Think you're missing a steel stamping which encircles the ball at the bottom of the shift cane. The tang at the "three o'clock" position, in this photo, fits in a groove in the ball on the shift cane, and there are two raised areas in the steel stamping which are clamped and located in the shift lever housing. A '37 and the '38 shown are slightly different. A working '30 or '31 shift mechanism will give you what you need. Best regards, Tom Hartz
Wasn't able to post the photo I edited to show the part. Sorry, guess I just hope my description will help. If not, I'm in the directories for
PAC, ACD, and CCCA.

West, you are correct, the seventh series had four speed transmissions. The difference is that in '31 there was a redesigned gearbox with third gear being constant mesh, and the shift to fourth was a "short throw." It seems funny that they did this as driving an 840 is a bit different than a Formula race car with paddle shifters, but I guess it was meant to appeal to people who were tired of shifting, as it was just a "short throw." Tom Hartz

Yes it's correct and in that position on Deluxe 7th & 8th Series cars with a lid on top. Tom Hartz

Mr. Cole makes some excellent observations about proportions Packard designers changed with the 8th series. Also, with the 8th they added an inch of height to the windshield with a different frame and posts for more headroom. Other instrument panel changes are glove box doors, the chrome across the bottom of the panel and the woodgrain finish. Steering wheel as noted is three spoke versus the "heavier" four spoke on the 7th. The 8th has wider front and rear springs, different manifolds with a small increase in power. A fuel pump versus the vacuum tank on the firewall. A four speed non-synchromesh transmission with "short throw" from 3rd to 4th. Seat cushion upholstery is slightly different. Wire wheels have hubcaps different from a 1932 but of the same diameter as on the 9th series. Disc wheels have larger screw on caps. Plus a few other changes.
A few years ago, I saw this interesting car, but couldn't decide how the fenders were changed. Were original 745 or 840 fenders shortened, and/or did they shorten the running boards? In any event it has the more graceful sloping fenders versus the original "spoon" shaped ones of a 740. Interesting discussion.
Tom Hartz