Hi Dan,
I had almost finished composing the following response a little while ago, prior to your post just above. I then had to leave the computer for a while and when I returned I see that a response is no longer needed. But since I had almost completed it I’ll post it anyway, FWIW:
If there are only two conductors in the cable, namely the shield and a single inner conductor, the shield would have to be connected at both ends.
If there are two conductors within the shield, one of those conductors would be connected to the center pins of both RCA connectors, of course; the other one of those conductors would be connected to the ground shell of both RCA connectors; and the shield would be connected to the ground shell of just one of the RCA connectors.
In the latter situation it would be best IMO to connect the RCA connector which has the shield connected to it to the component supplying the signal. I believe that is the majority view, although over the years I’ve come across a few opinions suggesting the opposite. It’s easy enough to try it both ways, of course, and you might even find that it makes no difference.
Best regards,
-- Al