I have a 96 Towncar and the windshield washer light stays on all the time, windshield tank is full. Any suggestions?

First, are there any other symptoms? Like:
1) Does the washer pump water?

The light is controlled by a float/magnet assembly inside the washer bottle. This operates a reed switch.

If the float/switch assembly is defective, the manual says it's not servicable and the whole bottle needs to be replaced.

I would try giving it a whack to see if the float is stuck....

Then I'd unplug the connector at the bottle to see if that turns off the light.

I imagine you could test the float/switch operation with an ohm or continuity meter.

The switch closed sends a signal to the wiper module, which intern operates the dash light. With that said, it may be a defect in the wiper module as well.

Towncar hit it right on the nail with a simple procedure to diagnose it. They usually don't fail but it is known to happen.

If you don't want to pay the high $$$ at the dealership, search out a autorecycler that deals with late model cars and get one and test it there (only takes 5 minutes remove, two bolt on the drivers side fender).

I think you could use one from 1991-1997 even later if they did not change the design or connector.