I haven't been able to find a 3D designed backplate/mount for rail buttons that will sufficiently hold a rail button to a rocket. AFAIK, this is the first one of its kind. It is designed to hold 1010-size rail buttons to a rocket and be low profile enough so that it will not interfere with the recovery system.

All mounts were designed based on the I.D. (inside diameter) of LOC/Precision rocketry airframe tubing.

The rail button plate is designed to fit a rail button nut into the hexagonal depression that is size 8-32 which is 8.52mm in width. I would suggest gluing in the nut, lining up the backplate with the hole in airframe, and then gluing in the backplate to the inside of the rocket. Just make sure you do not get any adhesive on the threads of the nut.

There are five airframe sizes - 38mm, 54mm, 66mm (2.56in.), 75mm (3.0in.), and 98mm (4.0in.).

Update: I printed (with a raft and support) and tested this design and found that the nut and bolt would not fit correctly. Version 2 corrects the problem.

These mounts are compatible with commercially available 1010 rail buttons or the following 3d designed rail buttons:

1010 Conformal Standard Rail Button Rounded
https://www.thingiverse.com/thing:3178417

1010 Conformal Standard Rail Button
https://www.thingiverse.com/thing:3168920

1010 Conformal Aero Rail Button 1/2" (12.7mm) Standoff
https://www.thingiverse.com/thing:3153215

1010 Conformal Aero Rail Button 3/8" (9.53mm) Standoff
https://www.thingiverse.com/thing:3150150

1010 Conformal Aero Rail Button 1/4" (6.35mm) Standoff
https://www.thingiverse.com/thing:3125414

1010 Conformal Aero Rail Button 3/16" (4.76mm) Standoff
https://www.thingiverse.com/thing:3115148

1010 Standard Rail Button
https://www.thingiverse.com/thing:3067689