Ok, I tried, and I got no saponification at all.
I heated both the mystery oil and some liquid Drano to about 90°, then poured the Drano into the oil while stirring.
I should get at least some kind of fairly thick soap, right ?
I just get some kind of incomplete mixing of oil & lye (and water I think, as it's liquid Drano), but about the same viscosity and color as the original oil.
Eventually it separates completely into the two parts.
[Btw, can you add too much lye and ruin the experiment ? I kept adding lye until about 2:1, lye:oil, just to see what would happen, and still no soap.]
Anyway I don't think it's vegetable oil : although it looks like it, it really doesn't have the expected smell anyway.
Unless anyone thinks otherwise, I think I'll take it to hazardous waste - probably why someone abandoned it in the first place.