Sorry, by overlapping squares I mean in the UV editor the shaded UVs are not inside one square(say a white one), but instead they take a good portion of the upper right quad in the editor(thus overlapping many squares). This would lead me to believe that your repeater idea wouldn't do anything either, because already there should be more than ~10 black/white squares showing on the model...

The checkers obviously show up in the UV editor which is weird. Just not in viewport or render... basically they don't get applied to model?

My procedure was to first get the head off the body via seporation, then isolate just the right side of the head. After this I just planar mapped UVs, and they came out fine for a simple test. I then applied a blinn/lamb to the selected faces/object and then apply the checkers. The UV editor reflects all changes, both solid color when blinn is applied, then checkers when that is applied. Just no visible changes on the actual model.

Again, feel like I'm missing something stupid and mundane. I know it's not my software/setup because I can create any objects and apply textures no problem. Just this downloaded model... that's why I provided the link, maybe there's something in there that's holding me up that I haven't been educated about yet.

Thanks for the reply, and any further information is much appreciated!

[Edit - Have added picture in initial post to clear confusion]