A bunch of easy little problems, tackle them individually, 1 at a time. If your bowl is dry, then the seal in the bowl is leaking and allowing the vacuum to suck the water out of the bowl and eventually, air. This is why your vacuum pump needs to recycle. As it sucks the water and air in, the vacuum goes away and then the vacuum pressure sensor tells the pump to go on. and build vacuum again. Clean that seal first, it may only need a good wiping, if not replace and that will solve vacuum pump cycling and dry bowl problem
Water pressure is simply a leak or two somewhere, I have found many during the 3 Grady;s I owned. Luckily they are usually at the end of the hose and only require tightening a clamp. Start at each faucet and check the hose (cold and hot) for leaks) don't forget the outside sink and rear shower. You will find each leak and that will prevent the pressure pump from cycling.
The full holding tank has nothing to do with the above and is a puzzle. Water is either entering through the discharge as cap as noted, or through the toilet if YOU keep adding water to the bowl while it is leaking into the holding tank.
Your discharge light? no clue.
I am probably the guy you read about with the clogged vent line. That caused some issues for me (including cycling). On the first boat, it was paper that made its way into the line when it was overfull. On the second, it was the vent screen in the vent that goes through the hull. Use a small pick and rip that screen out. The screen serves no purpose other than to clog. PPl say it will keep out flies but I have never had a fly looking to enter that (lotsa chemicals) and if they did fly into into there and then crawl the 3 ft to the holding tank, they would just die in there and get pumped out (but I have never had a fly there). Each time I pump out, I put my finger over the vent for a second to make sure it is pulling air from there (like your finger over the top of a straw).