Call me lazy but I'm not taking mine apart to see if there are 2 centrif switches, one for run hold and one for heat. Mine is a 120V portable besides, not necessarily the same.
It has 3 timed cycles, air, regular, permpress. Air of course is no heat. Permpress has a longer cooldown. No electronics and that's the way I like it. No relay either. In my previous fullsize Whirlmore I could hear it click behind the panel.
That it starts suggests the timer motor contact is good. The general current path is from plug, to door switch, to timer. From timer it goes to both start button and centrif switch so that if either of those is closed the motor runs. And the centrif switch keeps it running when you let go of the button.
Let's hope it's just a connection that needs to be pulled off and put back on. Otherwise the motor has to come apart or be replaced.