Thanks to all for your valuable problem solving input. Using your collective knowledge I was able to quickly solve the low voltage problem, complete the new toilet installation and enjoy the satisfaction of keeping "The Patriot" tip top.
It may be worthwhile to share the events leading up to buying, then DIY installing the new toilet. The factory original Dometic Magnum Opus was taking a couple of clicks on the rocker switch to get it to flush. The water fill was also working intermittently, but all worked well enough for months after first symptoms until one day all functions quit. I flipped toggle switches on the ridiculous circuit board and it came back to life for a few days before dying again. Lights were on and blinking on the circuit board, I could hear things clicking when attempting to activate flush or fill but it was dead. I called Dometic customer service, the CSR guided me through a few tests including a DC voltage (which read about 11.6VDC). The voltage reading raised no red flags for her and she proclaimed the circuit board kaput and obsolete. She told me their newer Dometic 4300 series is the new and improved replacement and explained it functioned much the same as the Magnum and they nixed the troublesome circuit board. She also told me a retailer, whom she would not name, had purchased a large volume of the 4300 series and was reselling them at a discounted price. With a little detective work I found it was Camping World. Camping World makes no mention of Dometic 4300 series in their description but instead refer to it as a Sealand Concerto P/N 26781, selling online for about $525.00 delivered after a 15% promo discount. It is indeed the Dometic 4310 that I received. I searched online and made some calls looking for a better deal but instead found the lowest price from other suppliers to be starting at $1000.00 min. plus tax and freight.
Now, the new replacement install. You already know how that started out for me, then I sought help through our wonderful BAC Technical Forum. Note that during every phase of my toilet odyssey the coach was and is connected to 50A 220VAC. With your guidance I went right to the toilet fuse on the 12VDC panel located in the bedroom closet. It's in position F10 as some of you advised. The ATC 10A fuse had contacts that allowed access while the fuse remained installed. On one side of the fuse, VDC read 11.6, the other read 13.XX. I pulled the fuse and tested across the blades, my DMM read a minute level of resistance instead of straight through continuity. I replaced the fuse with a new 10A ATC, the voltage on both sides of the fuse went to 13.6VDC. I went to the toilet, checked the input voltage, it was then 13.6VDC. Out of curiosity, I re-checked the original ATC 10A fuse. It read open that time. Apparently the filament was near failure and my handling finished it off. The new toilet functions perfectly and the physical design is enhanced.
Murphy's law came into play and remained in effect until I reached out to the BAC Technical forum. Naturally the failure accord 2100 miles from home in a rural area. We were, at least, in a comfortable RV park. We had the new toilet shipped to a nearby relatives house and it arrived freight damaged, the ceramic bowl broken into about 12 pieces. They ran out of stock but were expecting more in about a week. After 7 weeks traveling, we needed to be heading back home so had the replacement shipped to California. Traveling the 2K plus miles home with a non functioning toilet was inconvenient but not insurmountable thanks to a couple stops at Walmart for black tank de-stink. Toilet arrived a few days after we did, all in one piece.
As I finish my tale it occurred to me I have not tried my fancy new toilet with the coach unplugged and presumably operating at a lower voltage. Unless you hear from me otherwise, I am expecting all to go well. Thanks again for your help, I may have still been scratching my head were it not for all of your responses.