Electronic devices sometimes do that when they go bad.
It may be able to supply 106v with no load (or a very small load), but when the fan is connected, the amperage that the fan needs is too high for the (failed) electronic device.
The same thing would happen if you connected a high value resistor in series, such as a 270K OHM, with the 120v line and measured it with your meter, but then when you connect a load, such as the fan, it would drop to nearly 0 volts.
You could temporarily connected the Evaporator Fan to pin E3, so it only runs when the Compressor & Condenser Fan runs.
You wouldn't want it to run when the Defrost Cycle runs (if that still works)