I've burnished with a tandy bone, and wheel by hand.
I've used the smooth side of a scrap of veg tanned dampened and formed into a U for edges. I've also used dampened veg tanned to burnish the face of things.
I've used saddle soap and beeswax with my tandy burnishing wheel chucked into the drill press.
I've used gum-trag by and and with a machine.
For what it's worth... ALL CLEAR or see through soaps are glycerine soaps. In fact you can buy glycerine soap base in clear for about $5 for 2 lbs of the stuff.. plus shipping of course. This is the stuff soap makers melt, and add color and fragrance then pour into molds. Well, here is a 2lb batch for $4.15 plus shipping. http://www.bulknaturaloils.com/Products/15936-mp-glycerin-soap-base-clear.aspx
I did experiment with something I had left over from my "high maintenance long nail " days.... it's called Dry & Buff Polish dryer and glosser. ... it's in a nail polish bottle. I found the little brush to be handy and it appeared to burnish nice and shiny. However, when the edge was flexed or compressed the burnish returned to a semi-rough state. I abandoned any further tests though it did show potential. I think it might have been better had I slicked with soap or glycerine first, then used the dry and buff. I can't seem to find this stuff online so it might be a mute point.