Sorry guys; I'm an elecronics guy Digikey electronics; they have pretty much an electronic component you can imagine. I've designed a pet detector from there, lol.
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Yes, that's it. There's a tiny curved metal plate inside the switch. The curvature functions as a spring, and the plate itself also functions as a conductor. The button pushes in on the center of the plate, which causes it to contact a small terminal behind the plate.
Any time I pick up a shift knob, I check for continuity. On one of them, I had to take the button apart and lightly sand the terminals to establish continuity.
Those terminals are usually coin silver, so they tarnish. That's what they mean when they call those "collapsing dome" tactile switches, you can feel the little spring steel dome pop the other way, to make contact. At the end of their life, they don't pop back anymore.