How do nurses in retirement homes monitor whether an elder is in need of attention?

It's most likely a call button. Those usually have some sort of electrical device behind them so they can be transmitted to another floor or the like. It's not like ringing a bell.

The retirement home my dad lives in has call buttons in all public rooms as well as in the residents' private rooms and washrooms. They've also provided necklace/watch-like buttons for wearing if the resident/family/guardian opts for that.

In the nursing home my best friend's mother-in-law lives in, all residents have alarmed bracelets that are coded to specific doors. Some residents are bracelet-coded to set off alarms if they leave their room/floor/building - it's fairly easy to modify the coding as needed. Some are provided with attendant bracelets, similar to newborn hospital bracelets, so the resident can move around the building/grounds if they are accompanied by someone with a differently coded bracelet.

This is an area where technology truly is wonderful.

It can vary. There was a call button in one. But, when we moved my mother in law, the new home had a light to turn on.

My mother recently was in the hospital for a broken leg, she is 91. While in intensive care unit, there were electrodes on her body to monitor body function and it would set off an alarm if they went below normal levels. Also, there were camera monitors in her room. In the hallway, there would be a large monitor showing pulses of all the patients in the ward, so the nurses can see them. Later she was sent to a rehab hospital with less monitoring. Nurses just kept a timed schedule check on each patient. Patients always have a button to press to call the nurse.