Actually headlights work fine. They go up and down no problem.

The issue is when I attach the battery (it's out of the car while we rebuild)- the motor on the right side spins and makes noise for a few seconds. That's it. I'm sure that's not normal. I even purchased the little plastic pellet bushings just in case...
Are they maybe on their last leg or am I looking for another electrical issue?

 

Yep, most likely going to be bushings. I just installed a set of junkyard motors on my car (see the thread just below yours in the electronics section), and they had completely powdered bushings. Lights went up and down manually just fine, but motors just spun. Carefully pop the side covers off (the bolts like to snap, 7mm heads, be prepared to have to drill and tap), clean out all the nylon dust, and pop the new bushings in the gear. MAKE SURE you keep track of the washers in your motor assemblies, and put em back where you found 'em. There should be washers on the side of the gear armature that go between the top of the gear and the cover, and some that go between the bottom of the gear and the housing. Since they spin, you're probably going to be fine as far as the electronics.