Jaime, you are right - it very much depends on the time frame. So here it goes: The color specifications for Navy aircraft are given in a document called MIL-C-18263. This document has been revised multiple times over the years, the one of interest is revision B from Feb. 12, 1959. It describes a Fluorescent (High Visibilty) Color Configuration for four-engine and two-engine transport landplanes which operate predominantely within the United States, using Semi-Gloss Fluorescent Red Orange.
Please note the "transport landplanes" part - at least in my book the Neptune would rather qualify as a patrol or anti-submarine warfare aircraft, for which only the standard White/Seaplane Gray scheme was prescribed. Looks like someone took the "transport landplanes" scheme and slapped it onto the Neptune 🙂
In case you are interested in the further development: Revision E from May 11th, 1965 introduced Glossy International Orange instead of the Semi-Gloss Fluorescent Red Orange, from which point on only targets and drones remained in Red Orange.

In short: for your time frame the color should be FS28913

Cheers,
Boris