As far as shampoos and conditioners are concerned I would not use people products on him. You've gotten some good suggestions, cowboy magic as shampoo and MTG for a conditioner. MTG you do not rinse out. It won't make the hair soft and fluffy, but it WILL help any skin problems including dry skin and itchiness. You can just apply the MTG to the tail bone. To soften the rest of the hair of the tail I still suggest cholesterol.
I've never heard of the Lynn Palm tail bag...I mean it's a bag for the tail, a tube sock works too. But, becareful with the braid in 24/7/365. I keep my guys tail braided because the bone was docked and even though the hair has grown out it gets messy easy and it's more effective as a fly swatter braided since he can swing that around fairly easily. Braiding hair tightly, especially wet hair can cause breakage.
Most skin and hair problems are signs of poor nutrition. Evaluate the feed your guy is on, especially if this is a new place and new feed/hay for him. He may be used to more nutrients. I believe you board, so you may be unable to change what feed or hay he gets, but you mostly can add a supplement with ingredients that can help him. An example is Omega Horseshine -->
Horse Health Product Horseshine Omega 3 Flax Feed Supplement by Omega Fields
Also, as a final note your horse should only be washed when NEEDED. Horses need the natural oils they produce to keep their soft, shiny coats. Overwashing causes them to get dry skin which is then itchy. Limit the baths.