Did you scan the PCM first. if not way not. got DTCs'
not necessarily. "mont"
first learn what is there, there are 2 systems. old and new.
lets look at facts in the real fsm.
what is there,? (its new type.,like mine)
http://www.jeep4x4center.com/knowledge-base/index.htm?utm_source=cj#service

see page 2, in wiring wipers there.
see how that works, unlike what mont says.
The wiper driver stalk switch rarely fails.
The wiper has park sense, contacts.
the BCM watches those contracts and does the logic
via the BCM controlled, wiper on/off relay
so id pull that PDC relay first.

that act will stop it.
but not smack that relay hard, (dont wreck it )
then put it back, fixed now, good, get a new one soon.
now, the measure with any volt meter across across relay coil
0vdc is good, key in, wipers

12v dc means the BCM is confused, (it or the input from stalk drivers switch stuck on)



load side,
see page 1 in fsm
see that when MF switch is off, the high speed feed is 0v.
the BCM input from MFSwitch is infinity off, (no resistance)
at pin 8 of MFS, switch.
if the BCM sees a non open path the BCM will close the relay.
the BCM sees no connection or resistors or pin 9 stuck on high
or mist switch shorted.
that is how it works.

Has to be a problem with the switch. That's the only place they have in common. Well, they do often share the same fuse, so both are on the same circuit, but I think probably your switch for the wipers and the windshield washer.