Kyle,
Welcome to the forum!
I would order a master cylinder rebuild kit, a caliper rebuild kit, and then carefully pull everything apart.
If the brake lever has pressure, fill the reservoir, then un-bolt the caliper from the fork leg. Remove the brake pads. Insert a flat metal plate between the pucks and start pumping the lever to press out the brake pucks. Try to get them sliding out evenly and wedge a screwdriver in there if one is moving and the other one is stuck. That's the hardest part. Have an old towel handy to catch everything, the fluid will be dirty and corrosive to paint!
For the master cylinder, you'll need circlip pliers to extract the retainer clip and remove the guts. Make a note of what order the bits go in, and which side faces what.
Clean everything with brake parts cleaner, carefully replace the rubber bits and re-assemble using some clean brake fluid to lube everything with.
I have found hand-pump vacuum bleeders to be helpful, but it's still best to have an assistant when bleeding the system.
P.S. Removal and replacement of the rear brake master cylinder is Triumph's way of testing your manhood.