A sender will almost always fail in the closed position, a fail safe as it were...

Temp Senders are usually a wax type sender or bi metal in a wax or silicone filled bath.

Oil pressure senders are designed to fail in the closed position.

The flicker was the sender showing it was attempting to read and then failed closed-light on.

If you cooked it you may have breeched the head gasket. Check the oil for coolant or have the local shop run it thru the basic emissions test and see what the readings are. I found I had a head waterjacket to gasket failure and a wee warpage via this method after doing the top off deal for a month after my ex squeeze overheated the engine by idling in traffic with the AC set to Antarctic in August!

when you unplug the sender the lite stays on to tell you either it ain't working or the wiring just fried, either way failsafe to a definate error message via the low coolant light.