The switch on my 79 coupe started playing up.
It looks like that switch was used on all the XJSs up to facelift introduction.
It is fixable, but a bit of a struggle getting it out of the car.
Once out remove 2 screws and slide the steel cover to the left to release it from a groove in the plastic moulding.
There are a lot of little springs and things that could jump out at you. If you hold the switch over a big dish to catch any you should be O.K.
Take note of the location of the roller, the 3 springs and 4 little plastic "top hat" sliders. Note all 3 springs are different.
In my 44 year old switch it looked like the main problem was 44 year old grease congealing on the small copper roller that makes contact to activate the indicator.
A real good idea is to buy a small tube of electric and plastic compatible grease. You can buy them from Radio Spares or Newark and perhaps some electronic hobby shops.
The grease can be used to lubricate the 2 detent parts of the switch.
Putting it all back together takes patience. Make sure that roller is aligned correctly, it is hard to see once loaded.
Place the steel cover over the assembly and slide it to the right to engage the groove, and secure with 2 screws. At this stage to make life easy leave out the headlight flasher spring.
Check the operation of the switch. If correct remove a screw one at a time to fit the spring.

Yes, I know I should be whinging about the crappy Lucas stuff, but in fact that switch is a reasonable design for its time.
It does not have such a firm feel as most modern cars, but things do get better as time goes by ( well mostly ).

 

Great fix, and very usefiul archive material.
By the by, if anyone needs one, Manners have NOS stock of these switches at a pretty fair price.