This may sound like an odd question so I'll give a little background first. I'm a little OCD about flushing my tanks, ok ok, I'm A LOT OCD about flushing my tanks. I've been in a couple campers that...
So back to the OP question. We have a San-T-Flush, never use it, we use the wand you mentioned. Why... the San-T-Flush has fixed holes that spray the same spots If you have toilet paper stuck on a probe and it is not in the path of a hole it may not get it, the wand will. Our process, we dump, run the wand a couple of times, close the black valve, then put about 5 gal in and dump again usually comes out clean (through the clear adapter. Then I dump the gray to rinse out the hose.