I have an original Beeline without the 1/8 turn clip of the newer ones. I wanted to mount a Sigma bike light too. I have integrated bars that don't suit any of these mounts, to decided to adapt everything to the newer Beeline mounting system.
So, in the files are a basic interface plate for inclusion in your own designs and single and double versions of the mounting plate.
Also included is a glue-on adaptor (which I hot-glued on to my original Beeline) and an adaptor for the Sigma Halo bike light that I have.

The mounting clip prints pretty well in the as-installed orientation, with support. The flexure clips are well clear of the underside of the retaining tabs, so cleaning up the support is pretty easy.

The mounted versions have more depth and don't clean up quite so nicely, and definitely need support.

The swan-neck and mounts are designed for standard M5 cap screws and nuts.

This was based on dimensions from a friend with a newer Beeline. At this moment I am not 100% sure of compatibility with the actual Beeline parts, but this set here are all internally compatible.