I enjoy searching for Maker's marks and the like, so I've spent a fair bit of time on this one,
but I have nothing conclusive to add.
I do think the marks are a bit peculiar in that, each of the G initials appear to be from a different stamp - or maybe just the angle they were stamped at?
Also, the cross has a cross post like a Maltese Cross but the standard/upright appears as a straight pole - maybe signifying something with wings?
You are probably aware of this site,
Online Encyclopedia of Silver Marks, Hallmarks & Makers' Marks
It's a great resource for Maker's Marks and I've searched some countries' marks for you, but not all.
I did find a Native American Maker's mark site, with excellent information, and some potential leads, which I now don't think are viable - and as far as I am aware, the artists tend to work with Silver, not Gold (?) but maybe they are worth further investigation.

Here is the mark for
Gibson Gene, a Navajo artist.
I have seen a mention for Gibson Gene, on another site, that his symbol is 'peyote'
The same site shows a GG mark by an artist called Gertie Ganadonegro; not yours.
Indian Native American hallmarks G to L
Cheers, Mike