Internet Recovery Mode using Command + Option + Shift + R will boot the installer for the OS which originally shipped with the computer and hopefully doesn't include any new updates from the past week or so. This test saves you from performing a clean install since it is an older known OS and there are no third party apps to interfere.
I guess you could also try booting the Apple Diagnostics to look for issues. Use the trackpad to navigate and click items. This is outside any OS as well and could be another good test. Plus maybe the diagnostic will actually detect an issue with the Trackpad. I don't know why I didn't think of the diagnostics earlier.