There are analog clocks that move the minute hand only when the next minute starts. But to be honest, you might profit from a little less rigidity in your “time usage” - it’s good for your mental health to not plan everything down to the minute. If i make a private appointment, i try to set time windows of 10-15 minutes for meetups; i aim for the beginning of the window, and if i get delayed it’s of no consequence.

Can you imagine that it’s not so long ago that people called a phone number that told you what time it will be at the next signal tone?