According to the manuals I have, the J does not belong in the model slot.
Model codes for the 1959 F250 are F250 - 4x2, 7400 GVW F260 - 4x2, 4900 GVW F280 - 4x4, 7400 GVW F290 - 4x4, 4900 GVW
There will not be anything on that tag to indicate what a dealer installed.