First, the ground fault is somewhere in the building - hidden behind detectors, modules, horns, speakers, strobes, or just plain walls or ceiling.
Second, the ground fault light on the front of the fire alarm control panel is an absolutely terrible troubleshooting tool. It sometimes has minutes of delays in changing to on or to off; it is sometimes on when the ground fault is disconnected; it is sometimes off when the ground fault is still on the system. In other words; it will have you "chasing your tail" as you look all over in the wrong places. Don't even look at the ground fault light.
Besides, probably, the ground fault isn't at the panel; there's a very good chance it's somewhere else in the building. Running back and forth to keep checking the light wastes lots of time.
A Ground Fault is an Electrical Leakage Between the Fire Alarm System and Building Ground
When there's a ground fault, the fault is an electrical leakage. It could be a hard ground fault, like a copper wire in the fire alarm system contacting ground. It could be a soft ground fault leaking electrical current through worn or pinched insulation, or even a soft ground fault caused by water on the wiring or devices. It could be an induced ground fault like the magnetic coupling of power inside of conduits.
An ohmmeter can easily detect a hard ground fault. It's not so good with detecting a soft ground fault.
An insulation detector (which is an ohmmeter on steroids) will detect both hard and soft ground faults. Be careful with the insulation detector. If the voltage is higher than 40 volts, it can destroy whole fire alarm systems.
An AC or a DC Voltmeter can detect many induced ground faults. Sometimes, though, an oscilloscope is needed, although that is very rare.
By Douglas Krantz Check It Out
Troubleshooting - Detect the Ground Fault Without Using the Panel
You have to figure out how to detect the ground fault without using the panel. Take pictures of the wires and terminals on the control panel before disconnecting anything.
Disconnect both wires on the loop you're working on. If it's a Class A loop, disconnect those wires also. Before going out in the field, though, figure out which type of meter to use, and what to look for on the meter.
Use the Correct Tester and Make Sure you can Detect the Ground Fault
To easily find the ground fault, you have to use the correct measuring instrument, and then you can measure the ground fault. Without the correct tester, you're just making wild guesses.
Start out using your ohmmeter and check the resistance of each wire of the loop to ground.
Remember, it's the loop of wires in the building you're checking for a ground fault, not the panel. Don't check the terminals of the panel when looking for a ground fault, you could set off the alarms.
If you measure less than 100 ohms, you have a hard ground fault. You also have a means of checking for the ground fault. Go out and use your ohmmeter.
If you measure between 100 ohms and 100,000 ohms (100 KOhms), what you have is probably a soft ground fault. You can still use the ohmmeter, but take note of the readings. That kind of reading is what to look for.
If you measure more than 100 KOhms, use your judgement. That may be a hard to measure ground fault, or it may be just spurious measurements.
If it's a questionable ohmmeter reading, or open reading, switch your meter to AC Volts. Look to see if there's any AC voltage on each wire to ground, and also check just between the wires. There should not be any AC voltage on the wires. Reading an AC voltage might indicate a problem.
If there's no AC voltage, switch your meter to DC Volts. Make the measurements the same way you did with the AC measurements. There shouldn't be any DC voltage on the loop.
More resources on ground faults can be found at:
What is a Ground Fault?
Why Do Ground Faults Keep Happening in Some Buildings?
How Does One Find a Soft Ground Fault?
How Can I Find this Intermittent Ground Fault?
Can the Ground Fault Light be Used for Troubleshooting?