Seems like 12 unnecessary hours a year to me. Assuming it has a charging system, pretty sure it does, running it a hour a month at one time would keep battery charged anyway. Fresh fuel on hand, battery tender, and use it when needed is how I would go. Running it one hour a month just to keep it "limbered up" probably is not necessary in my opinion. REJ2.

Yes, the float charger is okay to use. If you're going to leave gasoline in the tank and carburetor, you should use stabilizer, such as Sta-Bil. My opinion (and this is just one guy's opinion) is that it is good to fire up any gasoline-fueled equipment from time to time; you shouldn't have to run it for an hour, though - 10 minutes or so will move gasoline through the carb, and let you know that it WILL start when you need it.

Some float chargers tend to keep charging at a low continuous rate as opposed to turning completely off. A gel-cell battery might not like that too much. I've had several batteries go completely dead from overcharging that way. I agree with rej2 that it may not be needed if you are starting it once a month. When you run it, be sure you let it go long enough to reach full operating temperature.

All emergency generators in fire stations that i've been associated with are run on a regular schedule, weekly or bimonthly to make sure they work when they are supposed to.
I think running monthly would be a good idea.It would keep the gas from evaporating from the carb & gumming up. Be careful with trickle chargers. Cheap one without electronics can still fry a battery by burning off the electrolite. I don't know about gel batteries though. Running once a month should keep the battery charged.
Use a voltmeter to check that the battery stays topped off from running the generator.

Thanks for the advice. I went ahead and removed the float charger from the gel cell battery. It was a high dollar charger I bought from Harbor Freight. $8.50 LOL. I'm not even sure it worked as my old 64 El Camino battery would still go down after setting all winter. I guess you get what you pay for. The generator is setting in my shop with the exhaust running outside. Yes I do have a carbon monoxide detector in my shop. I have a calendar in the shop so when I change the month I'll run the generator. If it doesn't start I can always use the pull start. Again thanks for the advice.

My generator owner's manual also recommends running it once a month, and to put a load on it by running some electrical equipment to keep the generator trouble free. I usually start it up and plug in my shop-vac and vacuum the basement.

Dave