Can anyone tell me for sure if Shimano 600 SL-6208 shifter and a Shimano 600 6401 (Trocolor) rear derailleur are compatible on a 6 speed rear cluster?

The shifters are said to be 6 speed and the rear derailleur 8 speed, but I'm not 100% sure if everything will work correctly together......

TIA

IIRC, the sprocket spacing and cable pull are different for 5/6 and 7/8-speed. If you replace the existing 6-speed freewheel with a 7-speed one it should match up. If you're doing a mismatched setup like this, it's better to make the 'extra' shifter position 8th rather than 1st. That way, if you accidentally try to shift into the nonexistent 8th gear, all that will happen is the cable will go slack. If you used positions 2-7 instead, trying to shift to 1st could stretch the cable or pull it through the anchor bolt, messing up your shifting.

I don't get this. As you point the spacing of 6s and 7s freewheels is different. The indexing comes from the levers and the OP has 6s levers and a 6s freewheel, so it will match as is. Changing to a 7s freewheel, will yield mis-matched spacing (as you correctly point out), and one unusable sprocket.

The fact that he has an 8s RD doesn't matter as much, since Shimano has been very consistent if the cable response ratio (how far the RD moves for any given cable movement) over the years. However if the RD and levers are many years apart in generation, the OP should confirm that the ratio is correct.

Yeah I misread it and thought we were dealing with 8-speed shifters. The derailleur itself doesn't really care, of course, as long as the cable pull matches the shifter.