Mack,
Sorry, been out a long, long time now, but some of the old phraseology sticks with you.
I am pretty certain now that the man we were talking about in the first instance, was a Flag Signalman, or as they were known to us seamen, Bunting Tossers, as mentioned before.
He would have been either a Third or Second class, Signalman, depending on whether he had another star below the badge.
In my day, there was always one on the bridge while at sea and they either sent signals by the use of flags or lamp (Using the Morse code). Mainly lamp by the time I came along, but signal flags at the masthead were still commonly used.
By the time I joined in the late fifties the trade badges had changed somewhat and they have changed again since I left. I was in the Radar branch myself.
A single Anchor (Hook), on the left arm denoted a Leading Hand and were known by the terms Hooky or Killick. (If you were liked that is)

Crossed Anchors on the left arm, denoted a Petty Officer.
If I could remember a quarter of the things I used to know, I still wouldn't come close to knowing all the things you have at your finger tips.
Long may you and the others like you continue to help out with all the things you do.
To me you are all STARS.
Thanks again
Tom