I wonder if there's a better way to refer to "hold on" music than say '"hold on" music'. It seems awkward to use that wording to refer to it, especially when you write an official text for a government agency. I wouldn't want to use it in a formal text.
The idiomatic expression—which most people will refer to it as—is simply on hold music. (Not hold on music.)
Have you ever wondered why you hear music or informational messages while you’re on hold? The reason is to give callers something to listen to while they’re waiting, right? Well, yes, but music and messages on hold were deliberately designed, based on the psychological reactions of people when they are placed on hold . . .
The whole purpose of playing music for someone on hold was originally to give a few moments between messages for the caller to absorb the message they just heard, for maximum recall later. Music serves the message, while also helping to pass the time. Not just any music will do, however; certain types of music calm a person while on hold, and other types cause them to react negatively. Justin Worland of Time Magazine discovered from a study in the Journal of Applied Social Psychology that playing recognizable pop songs produced a more positive experience for callers than elevator music or bland, repeating melodies, which tends to frustrate callers.
This is used in combination with on hold messages that will often play intermittently and interrupting the music. ("Thank you for your patience. Someone will be with you shortly.")
Many businesses play messages, music or a mixture of both for callers who are waiting to speak to a live person. An on-hold message is a speaking recording that lets the caller know she's still connected. A business may mix multiple messages or repeat the same set during a call, depending on its phone system message settings.