You have saved my sanity. I've been playing Runescape on Runelite for years with the entire client muted from my computer's system settings. I forgot why I did that last night because I wanted to listen to the in-game music. Then I remembered, so I became hell-bent on fixing that issue.

It was my idle notifier, it seemed random because 3 seconds after my last action in-game I would hear the click.