Windshield Wiper with a "mind of its own"

Windshield wiper turns on, works for about 30 seconds, and then stops in mid-stride. You then turn off the wiper, then turn it back on, and it works for about another 30 seconds. Intermediate does not work, slow speed starts and fast speed starts, but they only work for about 30 seconds, stopping in any random wiper arm position. (When set on intermediate, slow speed works, again for about 30 seconds.) What do I fix, the control arm on the steering column?. The motor is working, the wiper arm is working, just the brain has “a mind of its own”. Thanks in advance for your response.

Is this a GM car? If so replace the pulse board controller. It screws into the back of the wiper motor assembly. About $25 at a parts store.

It is a 1998 Jaguar xj8l. I hope that helps.