Seriously get a Haynes or similar manual, as from what I understand there is a rear subframe that you have to drop (along with the axle) - all tricky stuff
A horrible task
The entire rear diff unit has to be removed. It's a huge job not suited to non-professionals. Expect to pay for about 8 man hours plus parts and don't even think about taking this to a non Jag mechanic (so the hours will be expensive). Most Jag owners try to get as much rear end work out of the way all at the same time because removing and refitting the rear end is so expensive/painful.
The brake light switch on that bug would be found on the brake master cylinder. Remove the fuel tank to make access easier.
You will have to get a brake spoon and from the backside of the drum pull out the rubber plugs and look inside and you will see a gear wheel, the wheel needs to be turned downward to back the brake shoes off from the drum and then the drum should come off.
It takes DOT-3 brake fluid.
The Jaguar mfg 1940-1970's .177 cal 100%=$150, 90%=$110, 60%=$80
Under the hood?
My Chilton Volvo repair manual ( 1970 to 1983 ) shows ( DOT 4 brake fluid )
with a sledgehammer.
brake warning light
DOT ( 4 ) brake fluid , according to my Chilton Volvo ( 1970 - 83 ) repair book
I believe that the Jaguar XKE was first introduced in the year of 1961 and continued production through the early or mid 1970's. I think there were both US and British productions. Eversince I was a young person I have always wanted one!
Remove dust cap and wheel bearing try to pry off Try a wheel puller Try a big hammer and split drum
Push in on the bottom of the seat front and then lift.