This could be a bad relay or a problem with the GEM. The system is complicated with a ton of points it can fail (2 relays, GEM, run/park switch in the wiper motor, and resister bank in the stalk).
First check all fuses.
Next check the GEM ground located behind the center console. The ground is shared with the radio, cluster, and several other important devices. It is frequently messed up during a radio install.
Additional troubling shooting steps will need a set of wiring diagrams to best understand how the circuit works.
I maybe able to help with the diagrams. PM if interested.
2003 GT Convertible (sold)
2000 GT coupe (Craigslist project. Fixed. Now my DD). Windsor to Romeo swap.