On my current bike build, I'm trying out the FSA Wing Pro since everyone's raving about the comfort of flat top bars. I did a search, and it seems the popular choice is to not tape the flat part.

I don't have internal routing like on the carbon version. If I don't wrap it all the way, it would seem that the housing would flop around. Is there a suggestion to secure it against the bar without being unsightly?

I'm running Shimano shifters, BTW, so I only have the brake housing to worry about.

I have an alum ITM wing bar which is similiar to yours. I ran bar tape all along to the top because compared to a CF bar, I felt the formed area on top of the alum bar was not thick enough for my grip.
I have a Campy setup with two cables to deal with. My setup is comfortable for me.
You can use electrical tape underneath to secure your one cable prior to wrapping.

The Wing Pro has a groove underneath that the cables will sit in. So the cables are taped and then the short piece that is exposed sits in the area and should not move too much assuming that the cables are set up right. Like someone else said, you could always put a small piece of tape underneath to hold it in place. I had my bars partially taped and did not have need to use tape underneath the bars to hold the cables in place properly.