I was going to suggest a baby monitor.. The one we have is an angelcare ac401 and it has a movement sensor for monitoring baby breathing. The nursery unit is battery or ac powered and the microphone sensitivity can be set so that quiet noises don't alert the parent remote but loud ones do. The sensor is piezo based and detects the bed occipant breAthing and moving. After 30 seconds of no movement it beeps once at the nursery end to see if it can spark a movement and after about 10 seconds the alarm goes off. It can be quickly silenced from the parent unit. I don't know if you could use your electronics knowledge to extend the timer to an hour. A person (mum) in the nursery can control things simply by switching off the nursery unit which will prevent the movement alarm sounding but then she would need to unplug the sensor wires and take it with her and switch it on if she wanted to call for help. Not ideal for Alzheimer's sufferers
Perhaps an alternative is to build a device that mimics the movement sensor for some time when it is powered, associate it with the light she has to turn on to see her way to the bathroom. I used to live in a flat where the hall lights were on a push button that was on when in but slowly slides back out via some oil damper and Spring setup and turns off. Damping was adjustable. Electronic equivalents may exist and be better for turning light off earlier than timer expiry when bathroom break us over
I'm thinking when lights off and in bed, real movement sensor is working. Mum Wakes, turns on timed light, fake movement sensor takes over sending pulses to the monitor. Returns to bed, light off, real movement sensor is active again. If not returns to bed, timer expires, light off, real sensor takes over, no movement, alarm.
Or can just forget the movement idea and use her voice, put a whistle in each room etc. Maybe sew the whistle onto her nightie
Also I picked up a night vision IP camera in eBay for 20 quid once to monitor a bird nest that was in the way in my building site to make sure works elsewhere weren't disturbing them. Easy to setup, even has 2 way audio, remote pan and tilt to look around, iPad app etc, can monitor her from any where. Was gonna use it for baby but never got around to it.
It has movement alerts and other stuff you might be able to work up into a solution, maybe get a few of them and if the ultimate movement detected was not in bedroom in any 30 minute interval, ring a phone (Skype has a simple api for this, for example - when Skype is running it hosts a website. Opening a web browser to e.g.
Http://localhost:1234/dial/01234567890 causes Skype to dial the number). Any of the foscam clones on eBay will likely be suitable to experiment on, you can even borrow mine and have a play with it. I'm Not using it at the moment
Another good free app that uses cheap webcams for motion detection is called vitaminD.. Maybe has an api too so it could be integrated with some scripts that send alerts etc. One of many, to be certain
Oh and the angel care baby monitor unit has an Led light and a button intended for helping find a lost parent remote but it could equally work like a help button This nursery unit can be carried around when running on batteries and the audio part always works, but the sensor mat is a wired type thing so think carefully on whether you want to use it. The mode (movement sensing+audio vs audio only) can only be changed from the parent remote so if you want mum to carry the nursery unit you forego the movement: if it is in movement mode and the mat wire is unplugged the alarm sounds