Thermocouples produce a voltage output proportionate to temperature. You can take a good digital voltmeter and connect it to the thermocouple probe and measure its output directly. Note this requires the probe to be disconnected from the aircraft wiring harness. This same test can be made right at the engine monitor connector - disconnect the connector from the engine monitor and probe the + and - sides of the thermocouple. At rest in ambient room temperature the voltage produced should be quite small (at 70F it should be producing about 0.9 millivolts). As you heat the device its output voltage rises at a rate of about 41 microvolts per degree Celsius. That means at an EGT of 1500F it should be making about 33 millivolts.
Troubleshooting is fairly simple: stick your GOOD digital volt meter, set to millivolt range, across the output of the thermocouple, then heat it with a heat gun and see if its output voltage responds in a fairly linear fashion with rising temperature.
Good background reading here:
https://en.wikipedia.org/wiki/Thermocouple