'Mouse click' sound keeps randomly happening on Windows 7

See if it's the sound set to play under Control Panel -> Hardware and Sound -> "Change system sounds", the 7th from the end of the list - "Start Navigation". One of the first things I do on a new install of Windows is set that "Start Navigation" to "None" at the lower left corner.

If that's the sound, but you prefer to leave it on, it's going to likely be a long process figuring out which process (as noted by @DaveRook above) is "navigating".

Using Process Monitor, I found that sdxhelper.exe was causing this on my computer in December 2018. This executable is a background process used for updating Microsoft Office and is cryptographically signed by Microsoft, so it appears to be legitimate.

In order to find this, I started process monitor, applied a filter to path containing ".wav" and let it run until the click happened again.

One of my users had it. He was hearing the "C:\Windows\Media\Windows Navigation Start.wav" 2 times per second every time he opened some Office application, for example PowerPoint. His Office 365 password was out of sync with his Active Directory password. When he logged in to Office 365 with his current password then he didn't hear the "clicks" anymore.