On page 70 of Alan Raven’s “Fletcher-Class Destroyers” is a photo of the early style aft superstructure with a quad 1.1" AA mount. The director tub appears to be empty. Jeff Hearn states in his book that the Fletcher class ships so equipped with the 1.1 (Fletcher, Nicholas, and O"Bannon), had them replaced before entering service.
Was there ever any kind of director mounted there for the 1.1"quad? The photos that I have been able to find show (at least to my failing eyesight), at best, what appears to be something like a sky lookout chair.
Googling around, according to NAVWEAPS the MK44 was the designator which was associated with the 1.1.
Further at NAVSOURCE, the caption to a photo of the MK44 it states theat “since the limitations of this type of director would be further magnified by a platform as unstable as that provided by a destroyer, it had been considered advisable to install these directors only in the larger ships until the lead-computing type of director became available.” http://www.navsource.org/archives/01/57mk.htm
IMO, the director tub was left empty until the time that the improved director became available. When the 40mm replaced the 1.1 its director , the MK51, was placed in the tub. The gun tub was also re-shaped for the 40s.
This is a project Rick Davis and myself have been working on for a couple of years. The Mk 44 was one such director, but more common were the Mk49 and Mk 51 directors (and Mk 45 for larger vessels). The Mk 49 director was used on many destroyers; with Rick’s help I’ve been able to pop a list of them online. The Mk 49 page is here and the Fletchers under the Destroyers data tables.