Thanks both... I'll get a new battery. I would say it's been renewed twice I think, in the alarm's 13-year life, so as you suggest, it's about ready to pop its clogs. When it died last time though it didn't give quite the symptoms I'm getting now, but I suppose, if a circuit's supply voltage is low (assuming a low battery is either dragging down the supply rail or is failing to keep supply source impedance adequately low) unexpected results can occur.
Tony Johnson, Burton-on-Trent, August 2011