I found the Brookfield at a garage sale. The screw that was in the tree was broken off but the center pin is intact. Per information from Andrew Gibson, this tree bracket is a Holmes tree insulator. Style A (the smaller of the two sizes), and is the third variant in which it was made. It should have a metal strap holding a small split donut in place -- this is the style A3, circa about 1912/1913 I think as a possible start date, through to the end in the mid 1920s.