If anyone is still facing a similar issue with one of these older Cheney stairlifts, the fact that the chair moves when the reverser relay is actuated manually usually suggests the drive motor and much of the power side are still working. At that point, I'd be focusing more on the control circuit than the drive itself.
On older Cheney/Wecolator units, it's worth checking the pendant wiring, the connections at the terminal strip, and the direction relays or limit switch circuits that could be preventing the "down" command from reaching the relay. After years of service, it's fairly common to find corroded terminals, brittle wiring, or a faulty switch rather than a major component failure.
If you have access to a multimeter, tracing whether the down command is actually reaching the relay coil can help narrow the fault down much more quickly. Hopefully someone in the community still has one of the original Cheney wiring diagrams, as those have become increasingly difficult to find over the years.
If it does turn out that the lift is beyond economical repair and a brand-new replacement isn't within budget, it's also worth looking into professionally refurbished stairlifts. For many straight staircases, they can be a much more affordable alternative, provided they're supplied, installed, and supported by a reputable company with a warranty and ongoing servicing. Sometimes that's a more practical solution than trying to keep a 30+ year-old unit running.