[jhv48]

Mechanical gauges act just like a thermometer and should read the correct temp if the sensor is placed in a bowl of boiling water. Not dependent on ignition key or a ground.
Did this just happen or has it been like this forever? Usually when the hollow capillary tube of a mechanical gauge is breached, the gauge ceases to function altogether.

Are you sure the gauges are mechanical? There would be a protective wire sleeve wound around the entire capillary tube from the sensor to the gauge. If all you have is a wire to the gauge from the sensor, then you have electric gauges and the sensor will have to be grounded and the ignition switch on in order to test it.

Did you use some sort of sealer or tape to seal the sensor when it was installed in the engine? Sometimes that will inhibit a proper ground but then the gauge either works or it doesn’t. Your particular problem is a head scratcher. Both temp gauges failing at the same time is highly suspect.