I submitted runs for batman: the telltale series and none of the mods have been on in awhile and the 1 time I saw a mod online for for 5 mins and one day only. I would also like to become a mod, but I cannot contact any of the mods. What should I do?

It's very simple... if the game has total inactive moderators you should write your request in this forum:

https://www.speedrun.com/the_site/thread/dueac requesting for moderation in the game @JXjunk

Two of those moderators have logged on within the past month and they all have contact info (Twitch, YouTube, Discord, etc.). Adding to that the ability to message them directly on Speedrun.com, they'd have to try really hard to avoid you if you were determined to get a hold of them.