Did this trigger the other day, had to purchase a new 4-40 tap when the one that came in my cheap set wore down and wasn't cutting it, literally, even though I used oil.
The new tap worked great, got a bit worried when most of the tap went into the trigger housing. I didn't know how far I needed to get the threads cut. Stopped when there was some extra resistance, probably the tap bottoming against the trigger mechanism. The 4-40 set screw then screwed in easily after cleaning up the hole with a tipless Q-tip.
I don't have a trigger pull gauge, but I adjusted the set screw based on visually looking at the sear engagement through the hole in the side. Didn't want to set it too close to the hairy edge.