Instead of just connecting a wire, use your Multi-meter set to continuity and measure between the cases. Theoretically, it should be an extremely low resistance – somewhere between 0 and, say, a few 10’s of ohms. If you are reading a high resistance, then the cases (at least one of them) are not referenced to ground, or each other. At that point you can switch to volts – check both AC and DC – to see if there’s a potential charge between them.
If you are in the “good range“, you should be good to connect the wire between the cases to see if it helps.
