This same exact thing happened to me a couple of years ago. It turned out to be a bad Exhaust Brake Switch. Replaced the switch with a new one from Newmar, and problem solved. At Spartans' suggestion, I checked it by removing the switch and jumping the wires (bypassing the switch). The exhaust brake then worked fine, proving the bad switch.
You can certainly run without the exhaust brake. Just make use of manually downshifting with the arrow keys on your tranny when needed. Not as efficent as the exhaust brake of course and will require more attention to rpm's and speed, but it can be used to assist with slowing the coach. You won't hurt anything (the tranny computer won't allow it.) Heck, trucks had run for years without engine brakes.
When mine went out, I was a couple of hundred miles from home. No big deal. In fact, when I took my road test for my "R endorsement", I wasn't even allowed to have the exhaust brake turned on.