A keepsake for the exact time someone was born
Almost everyone knows their birth date. Far fewer do anything with the time.
The number nobody uses
Birth time gets written down carefully at the hospital and then sits unused on a certificate in a drawer. It is one of the few facts about a person that is precise to the minute and never referred to again.
That makes it good keepsake material. It is already specific, already theirs, and already carries meaning that needs no explanation to the person receiving it.
How a minute works as a keepsake
Claiming a minute takes it out of the pool of 1,440 and attaches it to one person, at a permanent address of its own.
Because the clock follows each visitor's local time, a claimed minute does not light up once and disappear. It travels, arriving in each timezone as that part of the world reaches it, so the same minute comes around through the day rather than passing in a single instant.
For a newborn, that is a record made on the day that will still be there when they are old enough to care about it. For an adult, it is a detail about themselves that was always true and never used.
A note on unknown birth times
Plenty of people do not know their birth time, and older records often omit it. If that is the case, the honest options are the time of the first photograph, the time someone remembers being called, or simply a minute chosen for them.
A gift that quietly invents a fact is worse than one that admits it chose. Pick deliberately and say so.