Activate location for "Find my Device"
In addition to enabling location services, the "battery saver" mode must be off.

In battery saver mode, location services will be automatically deactivated when the screen is off (Android Help). Unfortunately, Find My Device is not clever enough to deactivate batter saver mode for determining the location.

I did not find a way to use Find My Device while at the same time being able to extend battery life.