Sounds like my Dublin! I often wonder what he would do if they tried to chase him back!!
A word of caution, Helen. I notice in one of your pics the planter up close to the rail. You might want to move that so Mitzi doesn't get excited and go up and over the edge!
Dublin did that on my deck in his excitement of seeing a squirrel. Luckily he was on the portion of my deck that is just a few feet off of the ground, but I've learned to move everything away from the rail. He's such a stinking climber that I just don't trust him!!!