My GE washer won't fill on rinse cycle

Washer Repair
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1

Hi, my GE washer, model number WBSE2090A0WW fills, agitates, drains, and spins, but won’t fill with water on the rinse cycle. If I fill the machine with water myself, it starts working like normal. So, I am not sure if this would be a timer problem or maybe the solenoid? I have done a few minor repairs to other machines in the past and would like to try and fix this problem, if possible. Thank you in advance for your help and expertise.