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Never bridge where a Capacitor was installed, or any component for that matter, unless it was already a jumper to begin with. Just leave it off, and make sure none of the bits of it leftover are connecting, it'll be fine.
Those buttons are just active Lo like most of the others are.
With that little L1/L2 and R1/R2 FPC unplugged the L2/R2 lines are floating and weird things will happen. On the BWL-020 board there, solder a 10k from TP4 to TP6 (see the BWL-020, TRIGGER ASSEMBLY TOP image in the first post). That will keep the L2/R2 in the not pressed state, until you press your button, which will connect L2/R2 to ground and cause it to be pressed 100%. You can do that thru a 1k or less if you prefer.