I've seen alot of "mostly" early UV777's where the trem is touching the pickguard, not only squeaking when moved but also keeping the trem from returning to pitch freely, causing more erratic tuning return from a pull-up [not that the very fat knife edges and closed studs help on these UV's either]. I mention the knives and studs because this guitar did not have pickguard interference until I filed the mile wide knives and put in a set of open studs which moved the trem just enough toward the pickups that it came into contact with the guard. The first whammy down I heard it squeak and knew exactly what it was. When you have guard interference you will usually hear that squeak but not always, in which case it can be see on visual inspection.
Here you can more clearly see where the corner has distorted the curve of the guard causing a little bump.
This is quite easy to take care of. Just remove the trem following the instructions here and use a small round bastard file to cut the guard back. The guard cuts fast so take a few strokes and then drop the trem back in [without putting the springs on] to check progress often.
Once you have clearance be sure to file around that spot to put a clean curve back into the guard. Here you can just see the small gap between the trem and guard and under testing the trem does not make contact through it's full range of motion.
Blow away the filings, put everything back together, and the job is done.