They painted a Black curved panel on the sides, it was curved to the rear. naturally it got covered with oil. various planes differed in paint schemes - I think because they had a constant turnover of planes transferred from the fleet that were 'wearing out" so to speak, and rather than making mods at the depot or install upgrade kits by intermediate maintenance crews, they saved money by using them for advanced training. These planes were not "full up rounds" like their counterparts still in fleet service.
A lot of the painting of orange was likely done by the squadron. Probably the different schemes reflect various points where TRACOM dictated a scheme for various reasons, or maybe they painted transfers in increments as they were available to the paint crews.
MODEX's were assigned by TRACOM, at least the first number, per squadron - after that the 2nd and 3rd were usually incremental as they came in or replaced. Official records for maintenance and operations were by BuNo, however. MODEX was obviously just an easier way for quick reference by maintenance, ops and air traffic control.
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