We have a 50 gal black tank. If I left my grey tank closed, it would fill up many times more often than the black tank so I leave mine open. I shut it the night before I need to empty the black tank, do dishes that night, get up the next morning take showers, do morning dishes and wonder outside later in the day to empty both tanks and then leave the gray tank open again to repeat the process.
Depending on the size of both of your tanks and if you take showers in the RV, that will dictate how often you need to empty each tank and what course you want to take.
Bill