The car came with a bunch of receipts, showing it was painted in 1988. Also there was a tire receipt from 2004, which seems accurate. Up close you can see they aren't new, but still have good tread left. It's amazing what a little tire shine will do for the picture haha
I suspected the tires, since the car has been sitting for about 6 years. A couple of the tires have a slow leak, so they would eventually go nearly flat. But I thought that if the tires were out of round or "flat", then the vibration/shimmy would happen all of the time. Which is doesn't.
It doesn't change when braking, it is relatively intermittent, A few times I was accelerating pretty fast, got up to about 50, and had no problems. Other times it shakes violently at 30. So it is definitely an intermittent deal.
I waited six years to drive this thing again darnit! I guess it's not something I could've noticed when I first started the engine, since I only went around the parking lot a few times slowly.
Almost never any vibration below 30 mph.