I added an extra nut to the head of the screw so that there's a more substantial edge for the plastic can parts to press onto.

Screw the screw through the hole you've just created. It should stick out approximately 1/2" from the side of the mechanical assembly.

The 1/8" drill bit created a slight "interference fit" with the #8-32 screws, meaning that the plastic from the hole keeps the screw nice and tight.

Add a nut to the other side of the screw, just to hold it together.

Do not overtighten, as you want to keep a gap between the trap door and the side of the mechanical assembly.