That sounds like you got a tough job handed to you. First, do you WANT to be AM? It's not everyone's cup of tea. If you don't, that's ok. It got dumped on you without warning, and it is ok to ask other group members to take it. If nobody wants to lead, then it is ok to disband the group (with notice, of course) so you can be a fellow in another one. Or, do what Ashrem suggests, above. Merge with another group that has an AM who wants the job, and they'll be glad you don't want to fight them for the title.I understand that. Unfortunately, our Archmage had been away for personal reasons and had not been attentive. Then, one day last week she messaged me and said she was leaving and I should take the position. Then she disappeared before I could reply. I'm really not sure what to do.
If you stay as the AM of your group, determine what you'll call "inactive." Some groups use two weeks with no visible activity, score change, neighborly help, etc. Some groups are more strict, others less so. Make your criteria clear to the group, maybe ask them to help you define it if they're willing to give input. Then start enforcing the new expectation.
Players who you're sure are gone, you can simply remove. People you're on the fence about, write and ask them to respond if they are still here and want to stay. Then you can feel comfortable (a) that you tried to reach them, and (b) that your group understands you have a method and aren't just randomly booting people. Then you remove players who don't respond to your message, perhaps with a follow-up message that you would love to have them back if they ever return to the game.