When I braze up my own horns, 3/32" is OK for elevator if the span is not more than 1" each side of the horn. Of course, smaller models would get by with even less wire.  Span on flap horns is usually greater, so 1/8" is called for there.

I once made the mistake of using a CF rod for flap wire.  Not good.  Inside an aluminum tube, it did nothing but bind!  Had to tear it apart and install good old piano wire.

Floyd

I use 1/8 when I make my own, as Randy does, but I have been using drill rod instead of piano/music wire because it is bullet proof, but more easily tweaked.  No fellas, you can't tweak it accidentally, it's still too stiff for that.  But you stand a much better chance of not busting a flap.