MiddleMe

MiddleMe makes a three-finger tap on the trackpad work as a middle mouse click. In a browser that opens a link in a new tab or closes a tab; other apps do whatever they normally do on a middle click.

The app needs Accessibility access to read trackpad taps. Its window shows whether access is granted and has a button that opens the right settings. Once it's granted you can close the window: MiddleMe keeps running in the background and starts again after a reboot, unless you quit it with ⌘Q. Click its icon to open the window again.