Long term camping

Gray yes, black NO!

Black, NO! No that is unless you want to be digging a poo pile out of the holding tank.
BTW you must have a really small black tank to only last 2 or 3 days? DW amd I can go a week easily between dumps. But I simply dump on a weekly basis.
Yes, you can leave the gray tanks open. I normally close the gray valves the day before I plan to dump the black, and use that water to flish the lines.

Black tank NO, water will drain out leaving solids behind eventually plugging the tank

Grey yes and no. You can leave it open but would be better off keeping closed till near full so when dumping the black tank you can follow up with the grey to clean out the lines.

And now, you know the answer. :)

Thanks for the advice. Makes perfect sense. It is the grey tank that I have been having to dump every couple of days, I’ve just been dumping the black when I dump the grey for convenience sake.

That model has small tanks to start with
http://www.keystonerv.com/previous-years?brand=Outback&year=2005

Apparently both the black and grey tanks were 28 gallon, so on the grey in particular you will need to dump often especially if you are not being overly conservation minded.
If you are able to stay in place and connected just leave the grey open until a day before you need to dump black. Then dump both. A weekly schedule will simplify it some, but make sure you store grey for a day each time so you have a volume of water for clearing the black from your hose.

Wonder if we are the only ones who try to avoid putting solids down the stool? I think that prevents a bunch of worry and stress. Also, just don't like the idea of living right over human waste. We don't mind a short walk to the campground bathroom and try to avoid the furthest away sites. We're not fanatical about it as we will use the stool in our Class C if the weather is terrible, the campground BR is unusually nasty, etc. When we do have sewer connection, I don't even hook to it except for dumping which I do, both tanks, every 5 to 7 days. Never have any problems.

Also, I put a new dose of chemical down the stool after every dump.

“I’ve just been dumping the black when I dump the grey for convenience sake.”

Not my advice. Dump black when 2/3 to 3/4 full but you can add water to make it that full.

Guess I would never bring along my own personal toilet just to not use it, but to each their own.
In the OP situation, if black tank is toilet only, long term, I’d leave gray open most of the time for ease and whenever the black tank is getting full, let the gray fill up for a line flush and then dump em both. Be liberal with the water in the black tank too.