A bunch of micro-processors at play here. I am not sure if you are asking if there is a problem with light coming on and no alarm or what. Being parked and in neutral puzzles me.
In my case, a 2001 Newmar Kountry Star DP problem. We started on a trip and the light came on, loud alarm and gauge went to 0. Intermentent. When I took it in to Freightliner, they replaced the rear tank processor. However, there was an issue with that processor communicating with the engine processor and I ended up with 45,000 miles less on the odometer. Fed regs prohibit adjusting.
In your case, I wonder if someone disabled the warning. If so, I strongly urge you to rectify that because you don't want to loose pressure and not know it. Any way, you need to have it checked because of the above. Better safe with an irritating alarm than an actual issue without knowing it.