Bump steer question

What should I look for at the rear?

Same thing in the front.......looseness where it should not be. Get a "strong" friend, or if you are, someone else to look. Push it hard side to side and look for flex in the spring mounts, even U bolts and it's even possible you have a broken leaf. If the thing is jacked up excessively such as with air shocks, the excessive spring curvature/ arch causes them to be less stable side-to-side. This can give the effect of a low rear tire or cause you to imagine front end problems.

EVEN TIRE CHOICES between front and rear can make a vehicle behave horribly. I still remember working for a small outfit "back." He had a nearly new heavy half ton Dodge 78? 80?, was getting low on the factory tires. He had me buy two tires, I've forgotten which end. So two pairs of unmatched radials. The freeway is "a bit rough" (tracks worn in the pavement) and that thing was SCARY at any speed over 50. I went to the shop from the tires store and told the boss "that thing is not driveable." He had to buy two more new tires.