Hi, Geoff! I thought I'd add to your comments. Many plastic transistors follow the "emitter-base-collector" wire lead sequence, but not all do. Some have the base at one end or the other instead of the middle lead. Those tend to me transistors from Europe or Asia vs. the USA.
For checking transistors, I've kept an ancient, beat-to-hell analog VOM in my tool kit. I've used it enough to have a "feel" of how a transistor should "look" on the meter. I guess I'm a Luddite since I've had variable luck using a digital meter to check transistors in-circuit.
I'm glad you also reiterated the possibility of "bogus" readings with a component still soldered into the cirsuit.
Bri