Well, my TT does not have an engine, and it does not have a generator. But I do have a self-standing generator. I fire it up at least once a month. Even though it came with one of our previous TT's, I've never used it for camping. I have used it many, many times when power went off in the house. So I need to make sure it's always ready and working. So, once a month I fire it up, put it under a load (a light bulb or a power tool), long enough for the petcock to run dry and shut its self off when the petcock runs out of fuel. (That's about 7 minutes).
I have a gasoline log splitter, a snow blower, and 2 chain saws, and 3 lawn mowers. Through the winter I start them at least once a month. Sometimes when it's below zero, I cannot get them started, but I figure just turning over the crank case helps keeps everything healthy, and helps pumps oil to the top of the pistons and stuff.
Now my John Deere mower, also has a snow blower and I fire it up weekly! That beast is just too important to let the battery deplete any at all! I keep it going just like my car. It's got a water cooled engine (antifreeze), so my baby gets a lot of attention.
Any engine sitting is not good. They need to be stirred up every now and then. Decide on a routine: first day of the month, first Saturday of the Month, the 2nd and 4th Wednesday of every month, and just do it! Your engine will love you!