Something an old stereo tech friend does on TT issues;
1) flip the RCAs on your amp phono input and check if the music moves to the other speaker
2) check the cables from the TT and the RCAs
3) check the cartridge leads to the headshell
4) check your headshell, remove it and plug it back in, try to see if this makes a difference
5) check if the same scenario exisits when you play a different record
6) if you have a spare cartridge and headshell, try it, if the same problem persists, then it is your tone arm wiring or cables, if the same problem does not persist, its your cartridge wiring or perhaps your cartridge itself
The last time he saw this on this TT it was a loose wire at the cartridge rear end.