Short answer
What makes a good Mac menu-bar eye break app?
A good menu-bar eye break app should show the next break without taking
over your work, respect idle time or context, make skipping easy when
the timing is wrong, and avoid a cloud account for basic reminders.
Peeku fits that menu-bar-first, local-processing model.
For deep scheduling, Time Out is the more mature choice.
For polished eye-break flow, LookAway is the stronger dedicated app.
For open source, Stretchly and BreakTimer are better starting points.
For local Mac presence context, Peeku Presence Coach is built around no account, local camera processing, eye breaks, walk reminders, posture and distance nudges, and a quiet menu-bar status surface.