The state of the beacon isn’t anything to do with the world fuel. Unless you let the world go idle long enough for it to get deleted.
I think they offer a 4 week courtesy on the planet. After whatever the window is it doesn’t matter whether your beacon is fueled or not it’s going in reclaim.
I’m pretty sure it’s whatever you used to start the beacon. If you started your beacon with a greater beacon fuel it will go the 16 weeks if it was a campfire, you got 2 hours.
Also opening a reclaim on a placed but unfueled beacon apparently fuels it for 4 weeks as well. I assume that is what would apply to the gleam club expiry, if you started your beacon that way. I haven’t explored that.