In many of these tape decks DC cap discharges and gives +signal to control switch. You'll need to trace of switching + path and replace all of these caps without going to ID and testing them. Once one is down the other ones may 'keep company'. Chances that you won't ID the bad cap in the control PCB visually are high since we're dealing with frequent low-signal usage that is a factor of failure. Inventorizing small signal DC caps on the whole control board and replacing them may also solve the issue.
They may run $.05 each and they're not affecting any sonic performance as long as values and tolerance is kept while selecting the replacement ones.
They may run $.05 each and they're not affecting any sonic performance as long as values and tolerance is kept while selecting the replacement ones.