Kenmore Washer Spin Cycle Only Works Occasionally

So I just got a used Kenmore Washer and I’m running into an issue. Relatively frequently, the tub does not spin during a full cycle. Agitator, Rinse, and Drain all work fine, but sometimes the machine just doesn’t want to spin. However, if I stop the machine and restart it when it’s supposed to be spinning (not adjusting the timer from it’s current position) it immediately spins no problem.

I suspect the problem lies with the timer itself as it also froze up once on a different full cycle and didn’t advance for two hours, but I’d love some thoughts before I drop an additional $150 to test my theory. Apparently appliance parts stores allow you to return an unneeded part as long as it’s not installed (and somehow can tell if you’ve plugged something in once to test). Here’s additional info:

·         There is no lid switch- the switch has been bypassed.

·         The clutch assembly only turns when the tub turns (ie it’s not free spinning).

·         There are no unusual smells or sounds (other than clicking as it cycles (or tries to cycle) between modes).

·         I disassembled and reassembled the timer after pulling out the copper arms and cleaning the contacts with a whole bottle of contact cleaner (there are tiny plastic covers at the tips making cleaning the actual contacts with sandpaper extremely difficult). Problem still persists.

Any thoughts/suggestions are very much appreciated. Thanks in advance!

Update: just realized something potentially important. When the washer doesn’t spin, i still have to stop/start it to spin. However, if I stop/start it while it drains, it immediately starts spinning instead of waiting for the drain cycle to finish first. Makes me wonder if it’s an issue with the transmission?