Removing the TouchID button (for palmrest swaps following liquid exposure, presumably) is a pain, and if you damage it at all you’ll apparently need to get a new logic board entirely since the two are “married” as I’ve been led to understand. BE CAREFUL!
The button itself is mounted on a black metal shim-style frame/hinge that provides the button's pop-up action. The hinge's open edge is lateral (farther away from the center) and its connected edge is medial (towards the center of the laptop).
When removing and reattaching the button, you'll see that there are six screws to deal with - four silver and two black. The silver ones attach the button itself to the shim, and the black ones mount the shim to the frame. I found that the lateral black screw needs to be a little loose to give the button room to press in.
Also, spend a good deal of time being sure that your button alignment is proper - it’s really easy to have it shift or rotate slightly from its proper location. Don’t want to have to repeat your work!