Will - second of 2 gates in the clamps. Thanks to your encouragement, I got this one into the barely acceptable range - just under 1/64" out of square via diagonals measurement.
I decided I'll just tell the neighbor he must be drunk when he comments on the parallelogram of the first one.
However - I didn't have the "fortitude" to read all 8 pages of posts on this thread, but the few I did scan lead me to think there is a chance that this method won't tell me if they are square?? Something to do with string theory, effect of rotational dynamics of the earth on long wood fibers, and tin foil hats, I guess.
Heck with it - they ain't my gates anyway.
When I started woodworking, I didn't know squat. I have progressed in 30 years - now I do know squat.