The wipers on my '68 Deville never work when I first start the car.
Sometimes nothing, sometimes a small movement - maybe half way up the screen then they stop. After a few minutes they start to work perfectly and don't falter at all.
I've checked for all the potential earth and connection problems at both the motor and switch ends but can't find anything obvious - before pulling the switch and motor and stripping/cleaning/rebuilding it I thought I'd ask if anyone had encountered a similar problem.
I would think that the grease inside the wiper motor gears has dried up and become hard. I would remove the wiper motor, clean the gears on the inside and lubricate the wiper linkages.