Wired Ademco motion detector problem

Yup. Sounds like its relay is stuck. Just replace it.

It could be. Have you checked your connections? If voltage falls below a certain point on most motions, the unit will "open". The most common cause for a drop in voltage is loose or bad connections (sometimes from corrosion).

I could see that if the zone was held hopen but what about the light?

Maybe. You didn't say what type of motion detector it is; I'll assume it's a passive infrared.

Take a piece of cardboard and tape it over the front window of the detector. If the red light goes out, then the unit is seeing something in the room it interprets as motion. For example, hot air blowing right on the unit. If the light stays on even with the cardboard in place, open up the unit and look for bugs or anything else that shouldn't be there. If there's no obvious explanation and the light is still on, replace it.