Remember this is a ground thru the switch wiring.. The Positive is always on when key is on to the motor.
So yes if you have a bad ground thru the switch it may give you issues.
quoting Orge from this thread which has pictures.
https://67-72chevytrucks.com/vboard/showthread.php?t=733878"most pre-1980 electric wipers wire the same, power to the motor and ground thru the switch
the reason for this is the park function of the wipers
if you switch the power the wipers will stop where ever they are when the power is turned off
by switching the ground the internal cam switch keeps the motor on to the park area
the stock 2 speed electric wiper motor that orrieg posted has the switch on the motor and uses the same cable operator as the vacuum wipers
if your switch is a non-oem wired switch it will wire the same way; power to the motor and switched ground"
