Woody, I am not agreeing with what the neighbour did, just looking at the bright side. That tree grows right next to the bricks of your fence, not a good place at all. In years to come it would definitely have caused damage to the bricks. You have no evidence that it was the neighbour, so all you will do is hand the police another cold case.
If you really want to find out what happened, befriend your neighbour and in a year or so have him over for a BBQ , keep pouring the drinks ( he wont have to drive home so will enjoy ) and then you bring up the story of how a 'stranger' did you a huge favour by cutting that bastard Eucalyptus. He will then laugh and proudly tell you it was him that did it.
If you still don't like him then **** him there and then. If you happen to like him by then , laugh with him.