Shorted ends of various thermostat wires and measured loop resistance.
All seem reasonable ohms/foot compared to some new thermostat wires I have.

Measured the motor windings resistances.
High Speed winding 2.6 Ohms
Medium speed winding 3.6 Ohms.

Used a Biddle Megger set at 500 volts to check insulation strength to a ground at motor housing.
Both Windings read more than 1000 Mega-Ohms to ground.

I suspect either the “Fan Relay Contactor”
or the motor internal thermal protection switch.

A local supply house had a Packard PR380 Fan Relay for $12 (Made in China)
to replace the thirty seven year old Essex B12173-1 rated 12 full load amps.

I just installed the new Packard fan relay and the fan motor has run trouble free for one hour.

The 1/2 hp, 115 volt, Four speed, frame 48, 1074 rpm motor is marked “no longer available”
but I bought from Grainger a Century brand
3/4 hp four speed motor that shows the same shaft and exterior dimensions.