I guess I do not understand the question. When parked for a month you dump the tanks when they are full. Many who park longer term will leave the grey open until a day or so before black will be dumped and then close. After dumping black, grey is run through the hose to help flush it. We do not use deodorant chemicals, opting instead to use lots of flush water and Geo Method
which basically uses laundry detergent and Calgon softener.
If, instead, you are asking about dumping if parked for a month with not enough use to fill the tanks then you could add water to the black to fill it and then dump - best not to dump unless black is at least 2/3 full. When we are on the trip to our winter home tanks are dumped and cleaned the night before arrival and then used on the final day to our winter home where the motorhome is parked. There may be some day trips and weekend trips, and the tanks will get used occasionally when we are working on the unit or cleaning it. However, for the four or five months it sits we do nothing to the grey or black tanks unless we use enough to fill. Typically about the second day of our spring/summer travels is first tanks will be dumped after winter parking.