Patio screen door latch set

I have custom made sliding screen doors for a set of non sliding french patio doors to my deck. They came without any latch only pulls. Thay are installed as french sliders but I am willing to use the right hand one as a fixed door to allow me to get a working latch for the left side door. I would install a small bolt into the floor or ceiling to secure the fixed right door. The doors have a cut out area that could house a latch set adjacent to the pulls. What latch can I use? And what can I use on the fixed door in the cut out to hold it secure?

Here are some hopefully better pics.

The sliding french screens and non-french glass doors were manufactured by Gamco Corp. 131-10 Maple Ave. Flushing NY. They told me they did not supply latches with their screen doors because they mostly sell to commercial customers (?) Why commercial customers wouldn't want latches on their screens I don't know.

The square thing on the inner face of the pull does move up and down so it seems like there could be a latch hook thing inserted on one side and a strike/keeper thing on the opposite side.

Both sides of the french sliding screens have identical hardware,

I need something that latches so that you are able to both release and latch it from both the inside and the outside like a regular door handle. Will the 84-223 do this ?