I don’t think I would call a green on tan base a game marble, even when weak. I know of Heatons, Ravens, and JABOs with similar colors. Alley might be a possibility too. Ine of those makers likely
I bet I can help you with a list. If you can give me your email I would be happy to send you a Word document I wrote that includes all the known marble making sessions at JABO, SMM, and DAS. There’s some more details in it too.