I would look for an obstruction in the plumbing or an improperly adjusted or malfunctioning master cylinder. Also, I'd check that all the rear brake shoe springs are on properly. TeriAnn has a good page (or pages) on brakes on her site. Google "TeriAnn Wakeman land rover" if you aren't familiar with the site.
The brake light switch on the SIII is mechanical and it resides on top of the brake servo tower. Easy to get at and see what's going on with it.
Is your brake pedal retracting fully?
--Mark
1973 SIII 109 RHD 2.5NA Diesel
0-54mph in just under 11.5 minutes
(9.7 minutes now that she's a 3-door).