So i put together some PVC pipe as a twig holder.
Step 1: Get the pieces
1" Schedule-40 PVC pipe
2 x 12" = vertical
2 x 2" = horizontal
2 45 degree Elbows
2 x 18" = ForeArms
2 pipe clamps
2 2x5 mending plates
1 piece of 1x4 x 30" pine scrap
Total is less than 10 bucks at Home Depot
Step 2: Test the position on the fence
Notice how you can get the twine underneath and behind it to tie it into a snug bundle.
After you are satisfied with the dimensions, glue the pipe fittings together and stack and tie twigs.
I hope it works for you. It works for me. I'm glad that I finally got around to it.