Good, scan it first it is not a job you need to do for practice.

And I may even have a spare, Sergio has a reader, thanks Malcolm!!, will update when done

SPI it is probably the coolant temp sensor Peter.
Bit of a bugger to get to as it is under the intake, some say it can be done with multiple ratchet extensions from underneath but i usually remove the intake to change it.
If you have a ecu tester check the codes that may be stored. Remember if you have codes stored they need to be cleared with the tester after the repair, they will not clear by disconnecting the battery.

Even though the radiator was hot, make sure it is full.

Looking at the engine, look for a green/blue wire connected to a spade lug on the right, front of the cylinder head in the vicinity of the alternator.  Make sure the wire is plugged in/on the spade terminal of the sending unit.

If the fuel gauge is working OK, unplug the green/blue wire found above.  With the ignition in the run position, have a friend hold the brass terminal on the end of the green/blue wire against a bare metal bolt on the head (metal to metal).  If the temp gauge goes to HOT, the problem is likely with the sending unit.

If the fuel gauge is ALSO not working (see above) then the problem is likely with the voltage stabilizer OR the power supply to it.

Before I start troubler shooting, last night I climbed in the Mini, turned on the car and waited a few minute for it to warm up, the needle never moved and I started out, two blocks later, still no movement, stop the car look under the hood, no leaks, hoses and radiator are hot, normal hot,  climbed back in and drove home.  Deducted it is  an electrical issue with the temp sender or a blown fuse.

Any recommendations?  wire colors to trace?, connections to verify?, BTW, Rover Mini Spi, 1275 with an 88 degree t-stat, which is what that engine requires, the electronics are tough to follow