68 series 1.5. I installed a new temp sender because the temp gage stopped working. Now the gage goes into the red zone within minutes of startup. There are no overheating issues. I read that the gage can be adjusted on the back on the unit. The attached photo does show a slotted piece on the right side...but it wont rotate?...does anyone know how to adjust this?

 

Honestly, that one looks like it has "seen better days".
If the "slotted piece" on the right side you are referring to is the round item with the wire under it, that is a typical Lucas electrical connector hold-down nut, and to remove it it looks like you are going to need to use some penetrating oil. Otherwise it looks like it will "round out" on you, requiring the use of vice grips instead of a screwdriver.
To resolve your calibration problem, I recommend that you contact these guys, and see if they recommend buying a new gauge and sending unit as a set as I would:
:
Nisonger Instruments :: the exclusive Smiths U.S. Warranty & Service Center since 1949

 

I had the same issue after replacing my water temp sender. Not sure if it is worth trying to adjust the gauge, I just ordered another sender, placed it in boiling water to give me a trial reading before installing.

 

If you don't have the right sending unit then you'll get a bad reading. Start by checking to make sure you have the right sender for the gauge.

 

You may have a bad sender or gauge but a couple of other possibilities come to mind. The gauge is powered by about 10.5 volts from a regulator behind the dash. If it is shorted outputing 12 volts, an incorrect high temperature reading would occur. Check that the voltage at the gauge power connection is about 10.5v. Second, check that the coolant level is correct. If you loosen the sender, it should leak. If there is air in the manifold it will warm up quickly. Good luck, Bill

 

Were it me I'd buy a new gauge and sender: https://www.smiths-instruments.co.uk/jaguar Likely save yourself a ton of time and trouble, that gauge you have looks pretty bad.