My cat Casey is 9 and has never shown much interest in mirrors before, but
within the last 2 weeks, he meows to get to the bathroom vanity and look
into the mirror.  He is a Himmie and Himmies don't jump up higher than 3',
so he needs me to put the toilet seat down for a stepping stone to the
vanity to look in the mirror.  Gladly, I comply.

Before this, he jumped on the bathtub rim and climbed over the toilet tank
(and Kleenex box) to get to the vanity.

The toilet seat is much shorter.

He sits there staring for 3 hours at a time.  The longest so far.  He sees
his brother's reflection (he is sitting close by) and walks to the other
side of the mirror as if to greet him, and then he acts all confused and
goes back to his sitting place.  It is the funniest thing ever!  He meows
but doesn't paw at the mirror.

I have coaxed him to get away from the mirror after hours of sitting there,
and have lifted him off the vanity.  He jumps right back up (via toilet seat
for a step) and is studying things.....

My other cat couldn't be less impressed by mirrors.  I wonder what goes on
in his brain sometimes....