We Always Seem to Both Look at the Clock at 10:12

The number 1012 does have numerological meaning, as does the number 10 and the number 12.

Those numbers, along with the clock time 10:12, have personal meaning for you. They represent your birthday.

Numbers with personal meaning or emotional significance are the numbers most often noticed in the environment as a seemingly random event. Conscious attention is drawn to the familiar. The event of noticing the numbers is more likely to be remembered because of the associated meaning or significance.

When a number or set of numbers is seen again and again, and the person wonders if there's a special personal meaning to the seeing, that's when the person is likely to see the number even more often. See Why People Keep Seeing the Same Number Again and Again for an explaination why that is. Conscious attention is also drawn to the mysterious.

Regarding why Paul tends to also see 10:12 frequently, I can only guess. Perhaps he started seeing the numbers because you did, or because your birthday is special for him. There could be any number of reasons why he started seeing the numbers repeatedly. Almost certainly whatever the reason, it's associated with personal meaning or emotional significance.