I recently purchased a 1972 Series 1 XJ6, with 4 speed manual gearbox and overdrive.
On one of my first journeys I was diving down the motorway, I had engaged overdrive, which was working fine for 20-30 minutes. All of a sudden I could smell burning and looked down to see smoke coming from the overdrive button on the gear stick - not just from the transmission tunnel, but specifically from the button. I immediately disengaged overdrive, the smoke disappeared and I haven't used it since!
That is a clear sign of high resistance. Partial or complete short.
1. The switch itself.
2. Switch to solenoid wires.
3. The solenoid itself.
4. The connectors.