My go-to thong not only for everyday wear but especially the gym is the Obviously Anatomax thong. Obviously is currently going through a product refresh and the new thong version has not been released yet but the Anatomax Basics (Black, White, Graphite and Gray) and Downtown (Mint, Flint Blue, Slate and Red Brick) are still readily available direct from Obviously or through many of the online retailers including Amazon where you might save some money. A word about sizing...the pouch is the same size on ALL of the different sizes so the variation comes in the waistband and backside. Depending on your height/weight, you might want to select a small v's medium for example. I am 6-1, 170#, 32" waist, in the Basics I buy small and they fit perfectly in every aspect. Pouch does it's job, and the backside stays low beneath shorts, jeans, etc. The 'Downtown' model fits a little smaller so I wear a medium in that one and the fit is the same as the Basics. The other thing I like about Obviously is that the while the thong style is equal parts controversial and sexy (for the locker room), the underwear themselves are quite masculine, the colors are not too bright, the material is not sheer, and the pouch provides AWESOME natural support without lifting your junk up and making it stick out unnaturally which could raise a few eyebrows even with something over them. I also wear the Obviously jock (only size small though) as an alternative because somehow a jock in the locker room is more socially acceptable than a thong but I've never been a huge fan of the leg straps on a jock because they tend to roll up and that's not good for running as you know.
Another bonus is that they literally disappear under running tights and don't produce an unsightly bulge if you're running in a group.
https://obviously.com.au/discontinued-underwear/style/anatomax/thong.htmlOn that same note, a few brands to avoid at all cost...
2xist
Jockey
Anything bought in a department store especially in a multi-pack.