There is no "trick" to installing the button, if you seat the button (dangly bit down) and attach the bracket firmly, the button should click normally. The dangly bar is simply to keep the button level so it doesn't tilt on top of the pressure pad.
If you assemble the button and it DOESN'T click, then there is almost certainly an issue with your power cable.
Look very closely at the actual button (the orange blister in the middle of the bracket). There should be, barely visible, a tiny protrusion on the top. That's what the bottom of the button should be in contact with and making the little blister click. It is VERY tiny and barely visible, and also prone to breaking off. If that happens, you've next to no chance of finding where it went.
The correct solution is to purchase a new cable/sensor. They're pretty cheap.
You can also try to fix it manually, as I did.
You need a very thin piece of plastic. I used a bubble pack from a strip of Gaviscon tablets which seem to be about the right thickness.
Cut a tiny piece of plastic from it (about 1.5mm square)
Glue it dead-centre onto the little blister button. I used superglue.. normal glue was not strong enough.
This worked for me.. but the clean way to do it is replace the cable.