I don't think those flasher units are grounded to the case, because they have no ground. They are a switch. But even if they were, you would be getting a ground to ground. No short.
The thermal type are designed to work by producing heat, so if it got "stuck" it might just keep producing heat until it burned up.
You could just jump the socket with a small jumper wire and see if the lights will come on. They should burn steady. Obviously if it get hot real quick, pull it back out
Kurt