The black box on the motor, is just a terminal cover. The wiper delay box, is mounted under the dash near the steering column.
I would put my bet on the wiper switch.
after looking at them tonight in hand, the black box and the thin piece are called impulse bars, they tell the motor what to do via the points riding on the wheel inside housing.
i think you have to match the correct relay under dash to the correct impulse bar on the wiper motor,
this one i removed the cover from was gave to me and was supposed to have worked on delay, but I notice the impulse bar does not match my 85 square impulse bar which works on delay but stick and has run away for a while then un-sticks and delays...or they just stick and wipre steady for the long haul on delay mode.
the points fingers are not broke on this one, the greese is dry and caked up some but a little moving and re-lubing the gears with it is moistined right back up and should be good to go now. (mopar greese is the bestest greese)
you can see the circles where the finges ride on the wheel, and the contacs look good. ( i have seen them burnt and broke off)
here are some pics, the motor with no impulse bar should be the standerd 2 speed wiper, the skinny impulse bar motor may need a specific relay? the square box impulse bar goes with the green relay in the pic.
i just pulled my 85 harness and it has this same relay as the 85 harness i have as a spare, both had the square box impulse bar on the motor.
looking at the 2 motors i have, i agree they seem to be the same motor, just has a differt cover and wire hook up for delay than a standerd 2 speed motor.
I would also make a small ground strap to go from this ground screw on cover to ground strap on wiper motor mounting bolt, then a ground wire to the VR bolt and then to the engine block. i also run a ground wire from wiper motor ground strap to ground screw of wirehaness on the firewall and then to -side of BATT term for a good ground.
also run a ground from the -side of BATT to square metal box thing screwed to inside of dash that has the ground wires hooked to for the dash switch/lights ground, the key buzzer and wiper delay relay are both on this square metal dash grounding box.
never can have too many ground wires IMHO.
here are pics to study.