This is a watch my grandfather wore and I inherited (not sure where the watch came from as my grandfather lived his entire life in Barbados). Wasn't working when I received it and I had it serviced and repaired (left the face as is but overall in good condition). Replaced the strap. Keeps perfect time now and I wind it every day or two. I am trying to source the original box it came in via ebay etc. (so far nothing). Has hand inscribed numbers/letters on inside back case not visible to the eye (hard to see even with magnifying glass) Center of back face reads 43606 Other things inscribed toward the upper part (SWS 7810) and 1052016 c/o or m/s (really hard to read) and 7-96-W (really hard to read as well)
We have had this case show up a couple of times and identified it as the President 'H', and have also found one ad from 1964 (calling it the Squadron H).
Your dial is a bit different from this 1959 example, but perhaps it changed after a few years.
Also, your watch has a stainless steel back, but the President examples have a gold plated back.
I'll throw this out there to see what others think.
The subject watch has a number of characteristics of the Brigadier series from 1962/63. Key factor of which is the '23 Jewels' on the dial and SS backcase.
This watch may be another variant from this series.

The small scratches on the back inside case are from when a jeweler serviced the watch. The more scratches the better it was looked after. Each person had their own method/series of letters and numbers.
This is a puzzler. It looks like the known uses of this casing were the President that was 17J, and the Canadian advertised Squadron "H" was 23J like subject watch , but face is different.

This is the ad Ken referred to dated 1964, subject watch is 1963. Based on casing and jewel count as well as a one year difference between watch and ad, I'm inclined to say this is
most likely a 1963 Squadron - no variant, as it doesn't dial match the "H".
I also make note of the fact it may have had a different name for the US market if it was marketed here. If purchased in Barbados; a member of the British Commonwealth it's quite possible this is a Canadian named model.
I've been back and forth on this one, it's a wonderful keepsake from you grandfather. I'm not sure I can make a positive ID but am leaning to the Brigadier based on the stainless steel case back.
I am stumped. Could be a Brigadier or Squadron.
So I think we can ID as 'Unknown' for now and there is no general consensus as the the ID.
In reply to So I think we can ID as … by mybulova_admin
Sorry to say, I agree.
I've got one of these also. It's a 1963 model with an 11AC 23 jewel movement. It has a 10k rgp bezel with a stainless back and has what looks like the same "Flexon" brand band on it. I've had it for eleven years and it came from North Carolina. I'm inclined to think it's the Sqaudron "H". Perhaps the dial had a change in 1964.