Old joke - what do you find in Capt. Kirk's Toilet.... the captain's log.
The built in sprayer in the black tank is a bit wimpy - and doesn't exist in older trailers. They will flush, but not bust clogs. I remember metal spray wands from from years ago, so I looked up these in Camping World's site. The new ones are plastic, and can add a real boost, particularly if something strange was flushed like a small flashlight, a Barbie Doll head, glasses, dentures, etc.
The funny thing is that the WATER tank rinser looks like the ones I remember being designed for the black tank. And of two reviews for the "holding tank rinser", one noted that the nozzle fell off IN the tank. Not great design.
I who am not a germaphobe would buy two of former style, one for the water heater tank, and the other for the black tank. Keep the toilet one IN the bathroom to avoid contamination.)
Water Heater Tank Rinser - Camco 11691 - Water Heaters - Camping World
Holding Tank Rinser with Valve - Camco 40103 - Sewer Flushing - Camping World
In a pinch (and with a kiddie pool and short slinky, AND a face shield) you could "probe" the black tank from the outlet with one of these too.
and for those afraid to put #2 into the system, eat more prunes! (or drink more beer - purely as a stool softener you understand.)