Verify the following:
1: Check the operational state of the GFCI Receptacle in the Garage, by pressing the "TEST" Button.
If the "TEST" button _DOES NOT_ trip the GFCI Receptacle (verify trip by testing with Volt Meter), then the Garage GFCI Receptacle is malfunctioning.
Replace defective Receptacle with known good GFCI Receptacle (if withing your Service Work scope), then try the Motor test again.
If the "TEST" button _DOES_ trip the GFCI, then verify the Ground Pin of the GFCI Receptacle is connected to an Equipment Grounding Conductor / Bond, by using your Volt Meter.
Connect leads between "HOT" & "GROUND" Pins of the Receptacle.
No trip, or Voltage means the Ground Pin is _NOT_ terminated.
This could be a reason for the Motor not tripping the Garage Receptacle.
2: If the above tests result in proper operation, verify the Extension Cord's Equipment Grounding Conductor termiantions are solid on both ends.
If none of these verifications yield any abnormal issues, please reply with your findings.
Also include a little more information regarding the setup, such as:
* The Extension Cord test - are you connecting to the Branch Circuit at the Panelboard (Pump Circuit's origin), or directly to the Pump Motor;
* Ohm reading of Motor Windings, between L-G;
* Capacitor leads not providing path to Motor Frame, via small leakage path;
* Other types of leakage to Ground / Motor Frame.
I would verify the Ground Termiantion of the Garage Receptacle, as that seems to be the "No-Trip" issue.
Another test would be to install a Non-GFCI Receptacle at the Pump Motor (with the circuit connected as normal), run the Motor, and measure Amperes on the Ungrounded Conductor, Grounded "Neutral" Conductor, and the Equipment Grounding Conductor.
Do this at the Panelboard, where the Pump Circuit originates.
Verify the loads on these Conductors with the settings displaying as many Milliamps as possible.
If there is a difference of >5 Milliamps between any of the Circuit conductors, then the Motor has leakage issues.
Also check the Circuit with the Motor unplugged, and with the Pump Switch open, to verify the state of the Circuitry.
Any leakage >5 Milliamps with the Motor disconnected points to Circuitry issues.
Be sure the Client is willing to pay for this Troubleshooting, as it may take several hours to uncover the target problem(s).