Ok, the rear trigger is the set trigger.
The front trigger is the primary trigger.
The rear is supposed to be hard to pull, your pulling against the leaf spring that drives the rear cam.
The screw between the triggers adjusts how much the rear cam engages the primary trigger.
T/C will do nothing for you as they have stopped all production and service for these old cap lock rifles.
Remove the trigger guard, then remove the triggers clean them, lube them, and play with it in your hands, you'll see how it works.
(nothing will fly out or go "sproing")
It'll work in your hands just like it does in the rifle.
The screw that holds that leaf spring in can be adjusted with a small turn to change the amount of tension it applies to the rear trigger,, but you really do want it to be firm so it drives the cam quickly and firmly.
If you have a 93 or newer rifle, you'll have to remove the front tang bolt,, because it's used to hold the assembly in.
Older ones didn't have that feature the tang is held in with 2 wood screws.
And you don't need to be a gorilla when assembling, just snug things up, don't over-tighten,,
p.s. take the lock out too, clean it and oil it (and tighten those screws on that plate)