The common issue with these guitars is the vibrato system. There are many after market replacement systems on the market that are designed to solve the fact that they don’t stay in tune and that was the issue here. I adjusted everything I could to make sure that strings were no longer snagging on the intonation screws, checked the nut slots and I even popped a shim in the neck pocket in an attempt to raise the bridge up and increase the string pressure on the saddles. I managed to make some improvement and it keeps its tuning when you use the trem arm for light vibrato, anything more extreme the guitar goes flat or sharp depending on which direction you go.
