Exactly, in other words, the tone was there whether the engine was on
or off. This is why I am ruling out a fuel pump. I can't think of any
other buzzers or beepers that the car has. The lead to the positive
battery terminal did look as if something aftermarket had been
installed (an alarm system perhaps?) so I'm going to further
investigate to see if I can find anything. I'm still baffled though,
because the tone was way too faint to be an alarm, yet too loud to be a
keys-in-ignition buzz.