To perform a GFI test, start with the GFI cleared (if it's set, clear it. If it won't clear, the test fails). It should stay clear for a few dozen ms or so. Then, toggle the GFI Test line at 60 Hz (so change it every 8.3 ms) for 10 cycles. At the end of that, the GFI should be set. If not, the test is a failure. Wait 100 ms or so and clear it. If it doesn't clear, that's a failure. Watch it for another 100 ms. If it doesn't stay clear, that's a failure. If after all of that it hasn't failed, it's a pass.
This should be performed immediately before every attempt to turn the power on. Since the GFI is left in the clear state after the test, it's ok to turn the relay power on at that point and start toggling the power watchdog pin.