Finally got an email reply from moroso. It turns out that the thick shrink-wrap on the button (really thick!) was covering a threaded section with two little bezel nuts and a lock washer. I knew it would be something stupid! The plastic button pops right off and the threaded portion of the button is a perfect fit for the supplied bracket.

I'm not too surprised I couldn't figure it out- the shrink wrap covering the threads/nuts was cut neatly and was so thick it wasn't easy to get off. I couldn't tell there was anything underneath. Here's pictures:

And the switch with the shrink-wrap trimmed down: