This is what I just wrote on a British TR Foum.
I have heard stories about the rear cables that link this 3-pronged pivot device to the drums. You will have noticed that there is a long cable towards the left drum and a shorter cable to the right drum. The story goes that there are different design lengths between pre-TS 60000 TR3As and the post-TS 60000 TRs. I don't know if this is true or not. But when you assemble these cross cables and adjust the handbrake, you may find that you might need to alter the length of one or both of these cross cables by up to 1/4 inch shorter for it all to work at the optimum.
When I installed new cross cables in 1990, I had to remove the yoke ends, run a die up another 1/2 inch or so and cut off the extra 1/4" from the threaded end so it wouldn't jam, once I set the yokes to where the tightness was equal.
The cross cables should droop when the handbrake is not actuated and they should have equal "tightness" when the handbrake is pulled "on". Otherwise, one side may pull "on" before the other and may cause your TR to spin to one side or the other during an emergency stop. You can check this with the rear end up on jack stands and pull the handbrake on one click at a time - then check the droop or tightness. As you get to about the 5th click on the handbrake lever arm, the drums should have equal resistance when you manually rotate the drums. Then by the 6th click the drums should be locked equally tight. The 7th click is to take up slack and wear during the next 20,000 miles or so. Then the long cable from the lever to the pivot arm can be re-adjusted to re-set the handbrake properly.
Remember that these are "fly-off" handbrakes - the reverse of every modern car handbrake method since about 1965 or 1970. The early TRs were designed for rallies and racing as well as for fun touring and to swing the rear end of a sidescreenTR around a curve in an Alpine Rally or Mille Miglia, the driver could pull on the handbrake lever, perform his swing around the curve and then he just had to let go of the lever arm to continue.
When I park my TR3A in any public area, I pull on the hanbrake to the top. Then if someone wants to steal the TR, he doesn't know how to release the lever arm - so he gives up. Another anti-theft device.
Don Elliott, Original Owner, 1958 TR3A