If my description fits, there are several possible causes:
1) Bad solenoid
2) Bad relay
3) loose connections,
Easy to sort out. Requires a multimeter or a test light.
Ignition on, motor not running, gearbox in 3 or 4 th, gear, turn OD switch ON. OD light turns on. Now test for 12 V at term C1, the Yellow/Purple wire, on the relay. (You might want to temporarily re-mount the relay with terminals up fr access while troubleshooting. Be sure to re-attach the relay, as it must be grounded for proper operation)
If you have 12 V at Term C1, the relay is working, but if you did not hear the solenoid click, you have either a loose wire at the solenoid or a bad solenoid. Solenoid is available from VB and is not too difficult to replace .
If you have no 12 V at Term C1, then you have a bad relay. Replacements for these special, 2 contact, relays are hard to find, but you can replace it with a much more common relay, either a more common Lucas 6RA relay (like used for the original Series V ALt circuit) if you want to maintain an original look, or use a modern, low cost ( $6 ?) relay you can get from any Auto parts store. To use either of these more common relays you need a separate resistor and diode. I can supply these, along with connectors that simply the whole process in a kit I sell for $10, incl shipping in the US.
See this thread for more details:
http://www.sunbeamalpine.org/forum/showthread.php?t=17211
Tom
P.S. The relay CAN be disassembled and repaired, but I have had poor results with that. Most recently I added just the diode to my original OD relay, which is another solution if the relay still closes the one contact.