Please clarify: What do you mean by "ground/neutral fault"? Do you mean that a green wire (i.e., equipment grounding conductor) and a white wire (neutral conductor) contact each other downstream of the GFCI device? If so, then, (1) with the load turned off, nothing will happen - no trip, and (2) with the load turned on, the GFCI will trip immediately.
I don't know what you are looking for in terms of "proof." But here is essentially how a GFCI device operates:
Current passing through a wire creates a magnetic field around the wire.
Current passing through the "hot" wire on its way to the load and current returning from the load via the neutral wire will each create a magnetic field that surrounds the wire, but they will be opposite in orientation.
If things are working normally (no faults, no leakage currents, no arcing or sparking, and no person touching a live wire), then the two currents (toward the load and returning from the load) will be exactly equal. Their two magnetic fields will therefore be equal in magnitude, and opposite in orientation. So the two magnetic fields will cancel each other out.
A GFCI device has a "magnetic field detector," nothing fancier than a coil of wire that surrounds both the black wire and the white wire. Again if things are working normally, the two currents will be the same, the net magnetic field will be zero, and the "magnetic field detector" will sense nothing.
Now let's assume that a person has touched a live black wire. Some current will flow through the person's body, and will return to the source via the grounding electrode system. That means that the currents in the black and white wires, as seen at the location of the GFCI device, will not be equal. There will be a net magnetic field, and that will be observed by the GFCI device's "magnetic field detector." If the difference in the two currents exceeds the GFCI's limit (2-5 milliamps), the GFCI will trip. That is its purpose: to protect human life.
Finally, let's consider a green wire to white wire connection downstream of the GFCI device. This will place the two wires in parallel, since the green and white are connected to each other at the main panel. Thus, if 10 amps flow in the black wire, there will be 5 amps flowing in the green wire and 5 amps flowing in the white wire (give or take a small amount). Based on the previous bullet, you can see that the GFCI device will notice the condition and immediately trip.
If you need more "proof," then do an Internet search to confirm (or refute) what I have just described.
Neutral ground fault detection that detects and opens the circuit when there is a load side connection between the neutral and the EGC without any connected load was added a number of years ago but I am not sure when. I know it was before 2015. In 2015 UL 943 was modified to require automatic self testing of the GFCI, th neutral ground fault requirement was prior to that. This link has a description of how the neutral ground fault detection starting about 3:30 into the video.