Transmission Oil Temp. Light

New to Defender and cars in general so please forgive ignorance and dumb questions.

As soon as the ignition is switched on the Transmission Oil Temperature comes on and stays on.
Strangely it goes off when I turn the side lights on.

Any ideas what's going on?
Also is the vehicle still safe to drive at the moment?

Any help appreciated. Thanks

300 tdi ?as there isnt a transmission temp switch fitted so fault must be in dash or a fault with wiring loom connectors where they come through bulkhead near pedal boxes

A wiring fault would certainly explain why the light goes off when the side lights come on. I know the vehicle doesn't have it's original engine.