This redneck engineering is from over twenty years ago. I realize there are cool products available today. As a matter of fact they stole my idea.
Necessity is the mother of invention. I was fishing an ice out and was freezing cold. That nigh at camp huddled around the heat blaster I invented the very first dropper rig holders.
Get a 12-pack your favorite bottled beverage. Remove the corrugated bottle slats.
Separate and V notch the slat.
Hook fly to bottom of V and wrap until dropper fly hook positions on slat. Hook dropper. Hooking into corrugation, not through slat is best. Keeps another rig from snagging.
I usually put the fly with the bigger tail in the V notch. Or not.
Stack five or so together and stick them in your pocket. I wrap them together sometimes. Ten will fit vertically in a 5" sq disposable storage bowl and they fit perfectly in a pontoon, float tube pocket.
Amaze your fellow toon's by flicking one of these dropper rigs across the lake water to them like a flicking playing cards.