I grew up next to the NY&LB and, while my knowledge on the subject is far from comprehensive, I cannot recall seeing a 3 over 3 signal, particularly in the portion of the line from South Amboy to Middletown.
(pausing here to allow others to upload 355,000 pictures of 3 over 3 signals... 
)
The 3 over 2 worked just as you described. Since "L 133" (I might have that number wrong) was just a few hundred yards from my boyhood home, I probably sat and watched that signal work over and over again hundreds of times. Our biggest thrill when we were kids was to climb it and watch trains go by right next to us. It would sort of click and thunk internally as the lights changed colors.
If I had to guess -- and it's only a guess -- I'd say that the 3 over 3's might have been used in conjunction with any one of the numerous movable/opening bridges along the NY&LB.
HTH. Would love to see pictures of your layout.
Steven J. Serenska
