Well if you want to be safe change oil just before you park and again when you hit the road (Never did that but once, long story on that one)
Main engine unlike generator does NOT need monthly run
Generator needs regular exercise (Once a month, 1/2 hour 1/2 load or more in both half cases) for assorted reasons. some electronic some mechanical
The carbureted engines (Generator) are more senisitive to sitting than injected engines ..> You might want to add the prper Seaforam to the fuel tank for fuel stability.
Since the main engine can not be properly loaded. Running it even at fast idle is not good for it. The thing need to get up to full operating temp under load (Same for generator engine) when running. It needs to work, not just idle.