Whole house fan - unexpected voltage at high/low switch
To me it sounds like your switch is failing or arcing and not providing power under load.
Can you spin the fan? It should not be hard to spin  Just verify prior to the next step.
General purpose snap switches need to be 2x the motor rating.
Turn the breaker off
I would pull your high &amp; low connections from the switch and insulate 1 take the other directly to the power on the first switch . Turn the breaker on if the fan spins up get motor rated single pole single throw and single pole double throw switches.
The high voltage measured on low when the fan is on high is a “transformer type action “ from the different number of windings in high and low