96 Sable Intermittent Blower Motor Control

This strange problem occurred about three months ago. The blower fan (A/C Defrosters etc) only works when it wants to. Once it turns on, it stays on and doesn’t turn off by itself.

The switch for the fan is incorporated into the radio panel. It is “pressed” and not turned. (I am told that not all Sables have this set up).

When I start the car it’s the luck of the dice whether or not the A/C will work. Sometimes the blower starts upon pressing the switch and at other times it will remain off for five, ten, twenty minutes or more. Once it starts it stays on without a problem. I suspect there is a relay or some other device that’s failing. Any thoughts?

I have plenty of coolant, the A/C works well, but without a fan it’s useless. My electrical system is fine. Recently replaced the battery and alternator (this problem began for that repair).

Any help is appreciated.
PS: The car has 110K miles on it.