David Weaver
I wanted to do Autosol because it's better known, but I can't find my tube of it. What I do have is Dursol, which was sent to me to look at by someone a decade or so ago. It is more greasy than Autosol and more stinky, but otherwise similar. It has alumina in it, it hones, it leaves a film behind to lengthen the time you have to use it next as a metal polish.

First on a hard surface - cast in this case (instead of corian - corian just has no surface relief and the polished side is getting to be a pain to use).

Aggressive. I don't know that it's the dursol, it may just be having a heavy hand on cast and causing failures - who knows. At any rate, it's fast, but cast isn't the right surface for it.

on yellow pine, feeling that it needed a little relief and could stand having a slightly more forgiving background...

That's serious business right there. It's fast enough to be used as a finish hone by itself, though you can't bring too rough of a wire edge to it from a stone (it'll just scuff up the pine and maybe get embedded in it. The same thing happens to corian with a strong wire edge - it (Corian) gets damaged, too).

This is a practical option and with the right substrate -softwood or MDF, it's super fine. Subjective sharpness is about as good as anything you'll find and a pea sized amount will work over several irons. It's carried in some kind of petroleum stuff, so a drop or two of mineral oil or a bit of WD 40 will bring a dried up cake of it back to softness and usability again.