Next, we thought it may be coming from the bedroom slide. When I inspected the seals, we found a couple of possibilities so we closed the slide and waited for the next rain. With the slide close, it looked very tight. It rained again and leaked again!
This time, thinking I didn't caulk the roof well enough, I re-caulked and let it dry throughly. Instead of waiting for the next rain, I went on the roof with the hose and blocked around the vents with towels so water wouldn't go anywhere except over the side.
It just didn't seem right that it would leak after I did such a great job of caulking. I looked over the side of the motorhome and directly under where water ran down the side of the camper was the water heater enclosure. We ran water directly over the water heater and it leaked like a sieve. A little silicone caulk around the flange of the housing did the trick. It has not leaked during heavy rains in two weeks!
In summary, the next time we have to find a leak, we will localize small areas, one at a time, until the leak appears.