I'm assuming you have the optional (hidden) wipers and you have little experience as an electrician.
The wipers operate by grounding the Black and Black/Blue wires from the motor through the wiper switch which should be grounded. Make sure the ground strap behind the switch is grounded properly. Use an ohm-meter from the switch housing to a good carbody ground to verify.
Unless its defective, the wiper switch is hard to miss-wire but check the wiring (photo) anyway. Anything can happen in 51 years.
The 2 spade plug is for the washer pump. The Black/Yellow wire is the 12 volt source and jumpers to the #2
terminal of the motor. The Black/White wire goes to the switch and is the pump ground whenever the switch is pushed in.
If the wiper switch is grounded properly check the plugs (2) on the motor. Hard to see but they are to the lower right of the washer pump plug.
The single wire plug (Black/Blue) should go to the right. The two wire plug is to the left.
The two wire plug Black/Yellow wire (12 volts from the washer pump) should be to the right and the Black/White is to the left. See photo.
Photo of the wiper motor is from my El Camino and the wire colors are slightly different. Other photos are from my 68 GTO's harness (to be installed)