Video demonstrating some of the problem, the noise that isn't the key turning is just the air coming on because I left the switch on. Sorry for the bad camera work but it's the best example I've been able to film.
https://www.youtube.com/watch?v=k6Sv_9V9uT8
Basically, when the key is turned to on - even if the engine isn't turning - the speedometer climbs to between 13 and 18 miles per hour. This offset is somewhat random, and this is just the top and bottom values for the range I've observed. When the car is off, it slowly falls back down to the resting position, however it does this at very inconsistent speeds and doesn't seem to always go to zero, instead sometimes resting at around 5 miles per hour and not settling any lower. It seems to fall much slower if the car has been running for a while.
Under relatively normal acceleration and deceleration the speedometer will move at the correct rate up and down relative to my speed, and so it maintains this offset well enough to get an accurate reading of my speed as long as I remember it when I look. However, under rapid deceleration, the needle will move down significantly slower than the change in velocity, and will need a few seconds to catch up. Or catch down, I guess.
This problem confuses me and I can't really find anyone who's had something similar or who has a guess as to what it might be. I haven't been super extensive in my efforts to fix it so far, though, which is one of the reasons I'm making this post; I really don't want to start pulling things apart and looking around without asking first, as it'd suck to pull the dash off and then realize it's an issue that didn't require that, for example. I'm inexperienced enough with auto work that my efforts to diagnose in repair are as much a liability (via making mistakes fixing or via failing to correctly reassemble things) as an asset, so I want to get as much info as I can before continuing.
If anyone has relevant info on what this might be, what I should look at, and just any general info you'd think would be helpful, I'd appreciate it
Also, my first post here, or on an old style forum of any kind. Hi people! You all seem cool.