Oops...here is a picture of it....

I can't tell from your picture what sort of fence you have in your yard, but perhaps continue the veritical lines of the 1x1 spindles, just closer or one front one on the back of the cross bars and top the tall poles with a pergola. You have your grill there, so be sure that it doesn't get too hot. You could plant a bougainvillea on the opposite side of your deck, or if there isn't space there, put a pot to the left. That would create the organic element missing with just a wall, and increase the disguise of the proximity of your neighbor.

I would do a horizontal lattice-like wall which could easily be attached to the existing posts, the spacing depends on how much privacy you are looking for.

Love the lattices in Dytecture's photo. Visually, they are almost like shoji screens for the yard.