The 1997 Town Car diagnostics do not show a condition as you describe. Does the interval switch on the multi-function stalk switch work?
The wipers are controlled by the wiper motor which in turn is controlled by the wiper control module (called a governor). The module receives input from the multi function switch and instructs the washer motor and wiper motor appropriately.
There are tests for the multi function switch if you are up to electrical testing?
Attached are the required tests with access info. Hope this helps. The files are in alphabetic sequence. When looking at the wiper motor, check if there is a blocked drain causing flooding of the motor, on later models this caused unusual operation that was corrected by draining area and replacing the motor.