Run generator anytime you have a heavier load than just residential refrigerator and TV.
Also run generator if batteries get down to 12.2 VDC (at rest-- under heavy load does not count). Stop running generator if just to charge batteries when amps drop off below 30 amps charging. Said another way, the most efficient use of generator to charge batteries is to discharge to 50% (12.2 VDC) and recharge to 85%..... Yes, if doing this for more than a week, best to bring to full charge once a week, but suspect that will happen the next time you are on shore power or are driving all day.
Be sure the inverter is set to 50 amp on power share/power save to maximize charging amps.