So 2 weeks ago, I submitted 2 runs for Dr. Robotnik's Mean Bean Machine but they're still awaiting verification. I decided to contact the game's 2 mods by messaging them on this site and saw that one of them has been offline for 2 years and the other for 3 months. Since they were offline for so long, I decided to find another way to contact them and was only able to find them on Twitch. I decided to dm them there but it seems they've been offline for a while there too (One was last live 3 months ago, the other was a year ago).

So I was wondering, while I wouldn't mind waiting a bit longer, what should I do if none of the mods respond my dm and verify my runs?

https://www.speedrun.com/knowledgebase/supporthub/request-moderation

Fill that out, get 'em removed, become your own mod.

I forgot to mention one of the mods is mod for the Puyo Puyo Series and for some of the Puyo Puyo games he's the only mod, wouldn't that leave some games without a mod if I get him removed or would he just be removed from the game I request?

Just the game you request, I believe

Yeah, just the game you request. Either way it might be a good idea to make a forum post in those games warning future runners that he/she might be inactive.