I'm almost embarrassed to submit this because it is so simple, but a friend saw it in my place and thought it was a clever idea which others would appreciate.
Instead of a box of tangled test leads I've got an extremely simple organizer - a $1 wire basket nailed to the wall.
The basket was obtained at a local $1 discount store.
I used a handful of wire staples but almost anything will do - clips designed for coax cable, fender washers and drywall screws, etc.
Alligator clips clip to the basket's wires. Other leads are just hanging from the basket.