I, too, am a new member and I have had a GT6 Mk3 since March this year. The overdrive had been working fine in both 3rd and 4th gears until a couple of weeks ago when it stopped without any misfiring. This followed my fitting of a new ignition switch because the old one had fallen out of the steering lock housing. Being ignorant of the design I thought a find screw had fallen out and become lost so I purchased a new one only to find its a push fit into the housing with no fixings! Before removing the old one I photographed it and then re-attached the wiring as per my pictures. I also checked it against the wiring diagram in the workshop manual. It was then that I realised the wiring for the overdrive had no relay and was not as the later Mk3 wiring diagram. On the assumption that because it had worked before the ignition switch change there must be a wiring fault, I've spent the afternoon checking the OD wiring for continuity and that all three switches work and found no faults. On the solenoid feed I found insulation stripped in two small places, one of which could have touched and earthed on the body. I removed the plastic cap on the solenoid and as per the workshop manual checked the resistance on the series and shunt windings and found them to be as specified. So I took a feed directly from the battery to the solenoid by-passing the feed wire but it still wouldn't operate! My assumption is that there should be a relay in the system as per the Mk2 wiring diagram.
But is there anything else (mechanical?) I should check.
My intention now is to order a solenoid, relay and wiring harnesses from Canleys.
Next challenge is to release the hidden solenoid screw fixing!