Genoa staysail....
...is what you are seeing in that shot. Compared to a full sized, low clewed #1 genoa alone, the combo of genoa staysail and jib top (aka reacher, aka high clewed genoa) is a little faster but you give up 5 or more degrees of pointing.
It won't work too well under a more modern low clewed #1-the high clewed sail opens some room for this sail to operate.
On long races the consensus was a net upwind VMG gain with this setup over a single lower clewed genoa, but around the buoys it was a net loss-especially since tacking is so much slower with this rig.
Once you are truly cracked off from a beat it is much faster, and a nice plus is that you can shift down to a #2 (provided the clew is not too low), or blast reacher (high clewed #3 type sail) and still use it-which really does help keep the boat better balanced. Just remember it is not as close winded with this combo.
In the pic, the staysail is sheeted to a short staysail track on the cabin top, which is the best position for sheeting on this deck.
FWIW, the term "banana staysail" normally implies a tall, high aspect spinnaker staysail, which is hoisted on one of the spare genoa/kite halyards to nearly full hoist- and not a genoa staysail which is low aspect by definition, and generally not intened for use under a spinnaker. The term was pretty much out of use by the time the Schock 35 came into the world-although some of the old Santana 35's had them.
Spinnaker staysails, even the smaller high aspect ones, generally won't be effective any closer than around 90 degrees apparent.
This is just to reference the common use of that name, but we are all free to call our sails whatever we want of course!
For Jim McCone, I would love to have one of these on a furler (the type you can lower to the deck once the sail is furled), which I think is what your sailmaker is considering.
Cheers,
S