Thank you for your reply. Here are a few other pics. of this watch.
As you see my case does not have the lug holes.

: It's hard to see your case, can you post a pic from the side? But
: you are right, there does seem to be a similarity. The dial
: looked strange which threw me off, but you are right it is
: likely a repaint.

: A good source of info about Heuers from this period are the 1945
: and 1948 catalogs, hosted on the main OntheDash website. I had a
: look through these catalogs and Heuer did make a watch that
: looks like your one, the Ref 406, and it was available in 18k
: gold (becoming the ref 416) or 14k gold (becoming the 415). So
: it looks like your watch could be based on the Heuer 416.

: Most Heuer experts agree Heuer made watches for A&F, though you can
: read the heated exchange in a recent posting in the forum about
: this.

: For info, the watch I showed I believe was based on the Heuer ref
: 346; here is the steel version of the one I
: posted:

: And here is a reference 2444, also produced by Heuer:
:
: