Continuity can be tricky. IF, and I mean IF, it's possible to easily disconnect the wires going to the heat strips from the switch, then you can try for a continuity test. BE SURE all power if off at the circuit breaker. You need to electrically isolate the heat strips from the switch to make the test.
Another way would be to measure the voltage going to the heat strips. Again, be very careful and be sure the connections at the black switch are easy to get to with the multimeter probes. Assuming 240 volt heat strips, you should see 240 volts, AC across the two leads going to the strips. And you should see 120 volts, AC between each lead and the system ground/neutral.