Contact them on-site by posting in their forum or by messaging them. Or contact them off-site on Discord or in YouTube comments, for example.
Also on the game where you've submitted your run, 2 of the moderators were last online months ago and seem inactive. So, try to contact the active moderator, who was last online 6 days ago.
The 3 weeks / 21 days limit in the rules here shocked me. First I click on their profiles to see how many other games they mod. If it's not many then I DM them on this platform at 1 week. It's the letter icon. If they mod, say, 20 or more games then I wait 10-14 days. After 2 weeks, I look for a Discord they're members of or DM them directly on that platform.
At 3 weeks, you can submit a ticket to make yourself a mod or remove them from inactivity. I think the risk with removing is that mods tend to mod many games in the same genre and promote each other to mod status in the same friendly network. Be careful about making enemies. Posting in the game's Forum asking to verify makes them look bad imo so I haven't done that.
Other thing, their status showing they logged in 1 day ago but didn't verify your run isn't an argument to use against them. I don't have a life but other people do. I'd like to rules to shorten to 2 weeks to verify. If you can't do it then someone else can. Easy way to frustrate a new runner is making them wait and ignoring the Forum.
I disagree with shortening it to 2 weeks. I moderate a lot of games and get a decent amount of runs per week. For most games I mod, there simply isn't enough people who want to help or dedicate time into verifying runs, not to mention the occasional 4-8 hour runs I get sometimes. Hell, I'd even argue that it should be extended to 4 weeks.
In short, I need that time. You don't need a run to be verified that soon.