John, I do hear the "click" as you describe as the motor coasts to a stop and I don't smell anything burning. I am inclined to go with your thought that somehow, somewhere, the motor is not engaging with some part or parts in or as the motor connects to the tranny ............. I wonder if the timer plays any roll in telling the motor to engage or disengage with the tranny at any or many points ?? and if something is stuck in "neutral" due to a "timer" issue ?? I wonder if that is a possibility ?
Greg if you do hear the motor running and then a **click** when it slows do to a stop, the start switch is fine. Unfortuantely if that is the case there is probably a more serious problem. It could be that the rubber coupler has worn off, but finding a replacement for that might present a bit of a challenge. Keep us posted when get the motor off.