My mother is old, deaf, and demented. Any ideas on how to get her attention so she knows I want her to call me?
Why not call her? If it's because she can't hear the phone ringer, you can get an extra loud phone ringer.
I think the paradox you'll find yourself in is that you'll need her to know that x=y (e.g., flashing light=call Busthead). My understanding (no first hand knowledge here so apologies if I'm wrong and feel free to correct me) is that short-term memory is typically the first to go.
My first inclination would be a display of some sort that you could flash that literally says "call Busthead." You can do that with a tablet and one of the dashboard apps out there.
There are flasher devices to add on to landline phones for people that are hearing impaired. iPhones have an accessibility option that flashes the light when receiving a call, I assume most Android phones can do the same.
Depending on the severity of her cognitive impairment, that could be a harder issue to work around.
Simple idea. One of those cheap ■■■ 'light boxes'. With a 12v buzzer and a smart plug.
"call me", flashing and buzzing. Can have buzzers (vibration) on a table / under seat etc.
A more expensive option could be a smart watch that could receive notifications,... But the display is small... Does also rely on her wearing it.... Might work for some people... But perhaps not here....
Doesn't always work. My late next door neighbor who I was acting as looker-outer-for was always forgetting to hang up his phone which meant when his family called they got the busy tone. They used to call me to check on him and I used to have to go around and ring his front door and tell him to put his phone back.
So something is needed that the person would not have cause (or ability) to interact with directly themselves. A flashing light or sign that they can't reach is ideal. And I only say this because the OP has specified the person has dementia.
I use for this same purpose, with my mother in law, Amazon Echo Show devices which allow me to see where she is, and talk to her.
Their “drop-in” capability allows to connect with her without her needing to do anything.
Her TVs are connected to HE controlled plugs that I can turn off when I am aware that the volume is so high she cannot hear the phone or the Echo devices.
This combination has worked wonders for me.