Older Maytag top load washer will not fill with cold for wash cycle but does for rins

My washing machine will not fill with cold water for the wash cycle. Hot water flows for both warm and hot, and cold DOES fill for the rinse cycles. Everything else is fine. I can do a load of laundry by filling it with the rinse cycle then turn the knob over to wash and it will progress through the cycles normally. The only problem is that cold water will not fill for the wash cycle. Any advice would be greatly appreciated.

Since the cold water valve will work for cold rinse, this suggests the problem is either with the temp selection switch or the timer.

Current is not flowing to the cold water valve during the fill process.