First, what do you mean by the timer motor oscillating back and forth? It runs one direction only. If it’s starting and stopping, that a different thing.
The power goes from the power switch to the door safety switch relay, Then the fill timer, R2,
You want to check the door switch on the back of the machine. They often wear and click in and out. Watch DR relay as you move the door. The other thing is the extended run switch. The timer motor and light go through that switch. If that is stabile, but the light is still flickering, Check the 6 wire on the timer for stabile voltage. If 6 is stabile, but the light is erratic, Then the home cam switch is bad in the timer.
Manual and schematic. MH60 M3 112425 Pt1 (static-pt.com)https://static-pt.com/modelManual/CHA-MOY-MH-6M3_spm.pdf?v=1571247383299