OSR/NSR Tabletop Roleplaying Games

I like the simple faction system in Lavender Hack

Sandbox Generator has a good one as well

What makes these folk a faction is less about what powers they have and more about their active role in the world: what are they trying to accomplish and why?

It’s totally fine for these hermits to just be an interesting feature of that particular area— without any influence on the outside world— but, if you want to factionalize them, they need goals and motivations.

I like the concept. They sound like adherents to a god of lightning or storms. What might such a god ask of their followers?

I don’t have a direct resource but, Motive is important. Why would they do that? They’re hermits so I assume they don’t interact with each other much.

Maybe they’ve become drunk on power. They’re addicted to it. There’s something special about the mountain that allows them to do this and it attracts people that have some void to fill to it. Add in conflict. A nearby village has issues with them causing forest fires.

I think the main things to keep in mind is to remember that the factions' place in the world will always be defined by three things: their goals, their methods, and their history.

1. Their goals will bring them into conflict with other groups whose goals are at cross purposes, and will bring them positive associations with groups that share some similar aspirations. Are they trying to find a place to live? Well, someone already lives there. Are they trying to convert heathens? Those heathens probably already have their own religious organizations. Looking for resources? Maybe someone else is using them to harvest those resources in exchange for a cut. Etc.
2. A faction's methods can cause some division with other groups that sympathize with their goals but disagree with their methods or shared purpose with other groups that use related methods. Your hermits that use the lightning might be "good" but still abhorred by witch hunters. On the other hand, those "evil" blood mages that have been living underground for centuries might be inclined to help since they use similar magic, even though their goals might be unrelated.
3. A faction's history is easy: who helped them in the past and who hurt them. Grudges carry between generations really, really easily (look at Ireland, Palestine, or Native Americans), but so do memories of the groups who helped.

All this to say, when you start building the backstory of one group, their future goals, current methods, and past conflicts should make it pretty easy to see how their interactions can take shape. Just don't make anything too well aligned (or why are they even a separate faction) or too diametrically opposed (or it starts feeling contrived). History and relationships are messy, so your world's politics should be, too.

Yes

Worlds without numbers has a very expansive faction system, maybe that can help? It's free on dtrpg.