Here's another little gem from "Radio, Television and Electrical Repairs (Illustrated)".
Does this actually work?!
Well yes it does! - I found a small piece of potato from the kitchen waste bin, and poked two stiff copper wires into it. The chapter in the book was talking about lead-acid battery chargers, so I applied 12 Volts from the bench power supply and very quickly heard a fizzing sound and saw a halo of green appear around the positive connection. Looking more closely at the the negative wire I could see small bubbles appearing. I assume the green colour is some kind of electro-chemical reaction taking place with the liquid in the potato to form a green copper compound.
As for a "quick and useful" method of testing polarity ... I think I will stick to the test meter for now.