That is one sweet-looking squirrel gun. Is that a Thompson/Center? Details, please....
I also have tree rats in the woods behind my house. There are red squirrels and grey squirrels. There are also red squirrels with grey tails and grey squirrels with red tails. It's a genetic nightmare!
Fortunately for me, few ever cross the 600 yards of open field or come up the creeks on either side of the house to raid the bird feeders. Once, I had to chase a big tree rat out of the back yard by emptying the magazine of a .45 ACP at it while it beat feet back down to the creek.
Sorry, I misidentified your rifle; that's a T/C Contender. I've got a couple of those, too.
Ha, that's overkill. I use my .22/410 over and under with iron sights. I use the sub-sonic short .22 to keep the noise down.
And no, I don't use the .410 barrel on squirrels, I save that for Copperheads.