The power from the turntable comes from the AC line, but there is a solenoid switch in the circuit, driven from the cathodes of the output tubes.
This must be some sort of synchronization signal.
Solid state devices work very differently from tubes. To make another circuit, you would have to get that circuit working and analyze it.
When doing vintage restoration, it is basically vandalism not to return it to its original condition.
Your course of action usually ends up a mess for the above type of issues, and you end up with a worthless exhibit, even if you make it work.
My advise is to restore that unit to as close to original condition as possible.