With the old Thorens both the TT chassis AND the tonearm are often earthed to the same point - sometimes through the right channel, other times through a separate earth lead.
What I found when I separated the TT chassis earth from the arm earth and ran it to the AC outlet instead of the phono pre was a significant reduction in noise floor.
You should only run the arm ground to the phono pre.
You are better off to run a separate earth wire for the arm instead of using the right channel in my view - keep the signal cables as clean as possible.