I have to say straight off - I am not a horse/mule guy, but have been around plenty and rode my share doing backcountry range and forestry work for 12 years. I really enjoy this thread showing how to do it right. Every critter I have the "blessing" to ride had a weird phobia of some kind and it is obvious here that dedicated training and familiarization was lacking in all of those cases. High kudo's to you for sharing this. Should I ever trade my iron horse for a real horse/mule, I'll definitely be looking your threads up for pointers!
One would not step in or over flowing water - would only jump like a bronco over the creek but had no problem swimming the beaver pond when you weren't ready for it. One would let my daughters and female trainer ride, but never a male rider. One freaked out into rodeo mode at the sound of a map unfolding. Another was deathly afraid of anything white on the ground (bag, mushroom, hat, skull, shed antler, etc.) that was not snow. One would never lead on a trail, but only followed. One did lot like the sound of cicadas and got extremely jumpy whenever he heard them. One would not come close enough to an aspen tree to tie off, but had no problem at the corral being tied to the rail. The list goes on. The one thing they all had in common was I was always told "that horse/mule is old and gentle - you'll be OK!!"