In my experience, Ivermectin is the best as it will also get rid of red mite (on the body) and lice externally, and internal worms. Because it's absorbed into the body it has a residual effect so will kill all the red mite present at any one time, but not necessarily the subsequent generations.I usually dilute it about 5x with water and apply with a syringe or dropping pipette. I put some drops around the head and comb, a few on the back, and some on the legs. It soaks in fairly well on the legs where they are most encrusted.
Another old remedy is to soak the legs for a few minutes in a tin of paraffin or diesel.