You gain influence by occupying the town, pretty much the same rules for occupying a town as before (equipment, numbers, etc), which decreases the others' influence.
If people come in and mine and get to leave the map alive, you also gain influence.
The system is in it's early days, but I quite like it's potential. I didn't come up with it, so I'm not just praising myself

I think there should be some form of window reintroduced, so that X minutes per hour is all about protecting something from the other gangs, then the rest of the time is about guarding the town and making sure people can do stuff.
Then have the lockers looted more like once a day to the gang with the most influence, rather than every hour. Of course, increased to match the longer time period.