Yup, a secure socket on the square head is the goal. It will reduce that "tightening" effect when you cinch down the lock nut.
BUT, there are three different square nut sizes on that Tee... The one on the long end of the Tee is the biggest, might be good for the Honda Civic.
The two on the short legs are more like CG230 sized. I will verify the fit soon. Having a socket with a comfortable levered handle, THROUGH the locknut wrench is sweet
