I'm not sure if switching the fuel pump relay with an adjacent relay has anything to do with this

http://www.youtube.com/watch?v=RJrUmZ4sOyg

But just this morning I found out when I turn on my lights the wipers stop.

Can someone explain what is going on in the electronics that causes this and what's at fault?

Are the motors bad or something?

 

those two circuits are completely independent of each other electricity-wise, but they do come together at the wiper & hi/low switch in the steering column. the only thing I can think of is that somehow this switch broke and contacts are out of place inside. No guarantee, but its a start. Browse through over here, may help if you don't have the factory helms repair manual:
http://www.austinthirdgen.org/index.php?pid=19

 

woop. turns out it was a loose ground wire near the front of the chassis

Unscrewed it before to take off another ground wire that kept the secondary radiator fan on..forgot to screw it back on

crazy effect.