There have been numerous issues with the wiper motors as well as pulse modules on them. With the lights staying on, you can check the switches on both sides to see if one is shorted out and keeping the lights on.
things it could be.....the switch itself, the motor itself, a fuse, a relay or a poor ground on the motor. could also be the module but youve replaced it. my guess with out seeing it is the motor (most common)