I drove around my neighborhood a bunch this evening to test the speedometer and odometer and I’m super hyped to report that everything was in working order!
The new bulbs work well too, and what one is telling me is that the overdrive relay is probably broken. That’s the system that either allows or prevents the car from shifting into 4th gear depending on if a button on the side of the gear selector is pushed. Thankfully this part (previously mentioned as the white thing that needed to be pushed out of the way so the glove box could be closed) is cheap so it’s not a big deal.