I wonder if the shifter is on in an incorrect orientation. Referring to the spacer that goes over the shifter mount before you put the shift lever on: it has one big "key" on it, and this should be on the headtube-side of the stud. Those old 600 shifters could go all the way around if I recall correctly, so it could be 180 degrees backwards. Take the shift lever off and see if that could be the case.
It could also be that the indexing insert which has the D-ring on it has lost its "teeth," that shift lever seemed prone to this problem. These "teeth" mesh with the aforementioned spacer, and if they break, the shifter is going to turn under the tension of the derailleur cable. If this is the case, you'd need to find a shifter to cannibalize for the insert.