Actually, if there's only one Hopper only one half of the duo node is powered.
When my original 2H 1J setup was installed, only two lines were run inside from the Duo Node. Both of those lines went to Host ports. The second line had a tap installed and it then went to the second Hopper and my Joey. I returned the Hopper that was fed by the line from the tap, so the only thing on the second Host port was a Joey. Everything worked fine. I guess it's possible that a Joey is capable of powering half a Duo Node, but a SJ is not.
After this discussion, I moved the tap to the first Host port that feeds my Hopper. Both are now on one Host port. Not sure this was necessary, but I didn't want to risk overloading my Joey.