Could be a faulty motor switch. Can you provide a photo of the wiring diagram and timer chart? It's no longer available for that old (1988) model. Typically, the motor shifts to low speed for the last part of the agitation cycle. If there's a bad contact in the motor switch, it can cause the motor to continuously cut on and off rather than go into low speed.

Eric

Last 6 minutes of regular wash cycle agitation is low speed. Does the same clicking noise occur during gentle cycle? That cycle is low speed agitation only. If it happens there as well, it is most likely the motor switch. It could be an open low speed motor winding but that is rare. Disconnect the motor connector and check resistance on motor between the violet wire and the white/black wire. Should be a couple ohms. If it's open, the winding is bad. If it checks ok, take the cover off the motor switch and check the low speed contacts.

Eric

Can't say for sure without further testing. Those other contacts are for the start winding. Once the motor starts, it opens to disconnect the start winding. Since the motor is starting ok, they are working even though they don't look so good. When the washer goes to low speed, power is timer to motor via orange wire. With motor running, power via orange wire goes through the switch contacts to the violet wire (low speed winding). You need to check for any voltage drop across those contacts. The problem may be elsewhere such as a faulty connection at the terminal the orange wire connects to. It may also be a voltage drop through the timer contact for the orange wire.

Eric