The problem with storing the unit with gasoline in it, is that gasoline "goes bad" with time. Gasoline, like most substances in common use, consists of a number of distinct components. You are familiar with this phenomenon, because there are some bottles and jars that you have to shake or stir before use, because the components separate during storage. Such as orange juice. Gasoline does not separate in a visible way, but the most volatile components, know as the "light ends" (if I remember right), evaporate. This is the part of the gasoline that turns to fumes most easily, and this is vital to get a cold engine started. Think of the light ends of the gasoline as the kindling for a wood fire.
And think of the many times you have seen a neighbor try to start a lawn mower first time in spring -- pulling on the cord a million times to no avail, cleaning the wet spark plug over and over. We say that the old gasoline is stale. This happened to a neighbor of mine some years ago. When I realized what was going on, I walked over and told him to go to the filling station for fresh gasoline. I could tell by the look on his face that he did not entirely believe me, but maybe he wanted to be polite -- he went for fresh gasoline. Moments after he returned I heard his mower start.
You can still use the stale gasoline so long as the engine is warm, or you mix it with fresh gasoline. (I've been known to use many-years-old gasoline salvaged from junk boats. I'll pour two or three gallons into my half-full car tank.)
Now, I mentioned fuel stabilizing additives like Sta-Bil. This product reduces that evaporation of the "kindling". This certainly helps. But for a year's storage, I drain it completely, and I put Sta-Bil in the last of the gasoline since there is probably some left that does not get burned.
So what's this "gum" problem? Well, I know less about that, but I assume that's the solids that are left of the gasoline after all the liquids evaporate. Nasty stuff, for sure. So leave as little gasoline in there as you possibly can.
Then store the unit in a dry place, and minimize temperature swings. A basement (if it is dry) is better than a detached garage. You want to avoid condensation in the tank. Condensation -- moisture -- will corrode the tank and the carbonator. That's why some folks say to fill the tank full -- it will minimize condensation. But then you may have to drain that gasoline, and you may have more gunk than necessary.
Starting the generator every so often does not make sense to me. But I have heard reasonable-sounding arguments for that too. ("There are no answers, only choices.")