What's the part that is shaped like an L, has a rubber grommet on the bottom leg that fits into a slot just inside each end of the bumper (there is on on each side) and that bolts onto a bracket sticking forward from the fender on each side?

Mine is a 95 2wd 4R and we're talking about the factory bumper.

I need a new one or two new ones as the rubber's all worn out and the squeaking is driving me to distraction.

 

it's bumper to fender mount. it's there to secure the outer edges of the bumper since they're pretty much only bolted from the center section (aside from these tabs). i don't think it has any special name since it's welded onto the bumper metal, at least mine are on my 93. you might be able to find a replacement rubber piece for it. i'd take one off and go to dealer or parts stores, even hardware store, and find something that will work. salvage yard might have one too. might be called a "bumper to fender bushing"?

mine's driving me crazy because that's what my driver's side tire rubs on when I hit a dip while turning.

 

Yep, I think I'll just make one minus the rubber bushing to hold those two pieces together. Maybe I'll just weld it to the bumper and only have a bolt sticking through the tab on the fender. It'd be more sturdier that way.