The classic
SIIG MiniTouch has Alps or "Monterey" switches and the stabilizers on these are like Costar stabilizers.
I first attach the stabilizing wire onto the small white inserts. Then I make sure that the wire is on the right side when I attach the key onto the switch. When the key is mounted onto the switch I use a flat screwdriver to nudge the wire into the stabilizer mount on each side.
If something is wrong, then it is often because the small white inserts are facing the wrong way. If it is really tricky, then I often open the case so that I can better access.