When I pick up twigs and sticks, I stack them over by the fence, but by the time I am ready to tie them in a bundle, the bottom ones are weaker or wet and too messy to put a piece of twine under and tie a knot.
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
Try fitting on the fence somewhere and putting putting some branches in it.
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.