I keep meaning to respond to this, but also kept forgetting...

sorry....
The button is held on to the latch from behind, with a small screw. Chances are the screw is still in the seat. The problem is getting to it to re-install the screw.

To get to it, you need to remove the seatback, and peel the upholstery back on the top. Sounds harder than it really is, but it's still not a walk in the park. Once you have the back off, you'll need to remove the latch assy from the seat, and hopefully you'll find the loose screw(s) in there. Put the button back on, and reassemble the latch to the seat.

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Joel Adams
C3VR Lifetime Member #56 
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"Money can't buy happiness -- but somehow it's more comforting to cry in a CORVETTE than in a Kia"