I quite like it too (and see Tommy Lee Jones as the narrator). I preferred the second part as I found the first a little too rambling for my taste: black bear>narrator born>present>cat>bear>present>life history... It took me a couple of reads to get it all in.
The narrator's conviction that this will be his last year - that's based on the bells and past events, rather than being an idle idea? If so, I think more mention in the first paragraph of the reasoning behind it may hook the reader more, e.g.
I’m pretty sure that this will be my last birthday; the signs are there for my kind
(or something better than what I wrote).
But overall, good, interesting stuff.