Signal Flow of older AudioQuest Topaz

the one with one thick has shield connected to the ground.
that's the one you connect to the source.
that works if you have lots of RF arround your rig, otherwise you shouldn't bother.

I too have an older pair of AQ Topaz that I am cannibalizing in order to use the RCA's for another set of IC's. It probably wouldn't hurt to take the barrels off to make sure the rings are on the correct end (or simply the same on both cables) in regards to the shield being connected, as Marakanetz pointed out. Make sure you take out both set screws on each end before unscrewing.

I used the rings as a reference to keep them in the same direction, as arrows are used now. Once you've established which end is which you can experiment to see if there's any difference.

I had same question (with the same ICs) ... Asked Audioquest via email and was told: "The signal should flow from the single band (pre-amp) to the double band (amp)".

Gem's answer is correct, & yes it certainly makes a difference, assuming you know what to listen for.