I think part of the explanation is one of perception. We might be looking at the clock many times a day, but if the time is 13:56, we just acknowledge the time without attributing a special significance to the numbers. But if the time is 13:31, it changes, although in linear time it is only a short time span away - it is a symmetrical number. Or 13:13, or 13:33, or … there are many combinations of numbers that might strike a chord. In my case it is often symmetry.
My ’thing’ is 22:22 and 23:45 - but I guess the explanation here might be that this is often the time I go to bed, and while doing so, I look at the watch, so the statistical likelihood that I hit these numbers is small, but not that small.
I am not claiming that this is the sole explanation, but in my mind it is at least part of it.