Could you record a sample of the beeping for us? There are different beeps for different situations, maybe hearing it will help us figure it out.
Of course, I'm not ruling out the possibility of a fault in the instrument panel, which could even just be the result of a change in the stereo unit because a lot of Navaras share an earth between the stereo and the instrument cluster, and if the earth isn't perfect, it causes very odd issues with instrumentation. It's an easy fix - add a (black) wire from the frame on the stereo to a bolt that holds the dash in the car (easily found under the dash, there are several).