I have tried to figure out the electrical circuit, and it is possible that the relay is missing a jumper wire between the C4 terminal and the W2 terminal, or the internal contacts for C4 are corroded. The C4 to W1 connection “latches” the relay in the overdrive engaged state. Without this, the relay will disengage the overdrive whenever the throttle is closed. However, the overdrive would re-engage when the throttle is reapplied.
This failure would only occur if your throttle switch is installed and working. My car, as many others, has had the switch removed.
I found the internal wiring of the relay in a Sunbeam Alpine workshop manual:
When the overdrive switch is set to “in” and the mechanical throttle is not closed (causing the throttle switch to be electrically closed) then the relay winding is energized. This closing of the relay contacts means power is routed from C2 to both C1 (the solenoid) and C4, which is connected to W1. This means that if the throttle is now closed (causing the throttle switch electrically to open), power is still fed to W1 from C4, keeping the relay energized and hence the solenoid also energized.
When the overdrive switch is thrown to “out” and the throttle is not closed (so the throttle switch is closed), then W1 is electrically connected to W2. This connects the two ends of the relay windings - i.e. shorts the coil out - so the relay contacts open disconnecting power to C1, the solenoid.
I found this post giving tips for finding fault in the hydraulic circuit: [xk] 150 overdrive - #5 by Gary_Lindstrom.