"I believe you might be on to something because he said he could hear the relay."

Right, Phil.

And, I assumed he heard it click, not buzz. Assumptions are the worst pitfalls of communication.

Phil, have you ever heard a DC relay buzz? A relay that is supposed to be a switch turns into a buzzer when the source of its coil voltage gets dragged down by the current its contacts are switching.

The reason that could happen is high resistance in the source, such as would result from an oxidized or corroded connection. The buzzing, or oscillation, is the result of its contacts opening and closing rapidly because the coil pulls them together until the contacts stop the current to the coil and the spring pulls them back apart. Repeat.

"While he has something turned on in the car or the troubled circuit is nice."

Not just nice, but necessary. A modern meter does not itself pull enough load to show a diminished voltage through the sort of high resistance connection that would stop a car. That's where a test light can be a better tool, but the meter will be OK if the normal load is connected to the circuit being checked.
--
Art Benstein near Baltimore

I find it ironic that the colors red, white, and blue stand for freedom, until they're flashing behind you.