Anybody have a source or part to suggest for very, very small eye bolts?

I'm ideally looking for SS304/SS316, an M3 or 4-40 thread, an eye perhaps 5mm OD, and just a few mm of thread.

EDIT: Roughly speaking, imagine something with proportions like this https://us.misumi-ec.com/vona2/detail/110100190570/?HissuCode=CHI12 but a 4-40 or M3 thread.

It doesn't have to be very strong at all, I just need to be able to run a tiny string through it to secure some bundles of micro coax to, but I want something with a permanent screw attachment rather than relying on adhesive that might fail after a couple of years.

@azonenberg not sure there is anything that meets your requirements but maybe modelers have something that could work? Model ships have need for tiny lines being tied down in various ways. E.g.
https://www.midwestmodelyachting.com/Turnbuckles-Rigging-Screws_c_161.html