I'm unable to open the case
Access to the movement will be through the front of the watch. Check to see how the front bezel may come off, screw or snap?
haha my first thought after seeing first pic was a mystery beau
Will,
I think You're correct.
I know there's no ad for such a beast (Beau "mystery")....but there's no ad for any "mystery" now, and it does have some of the charactoristics of the Beau w/ that dial.
Still no advert for 'Mystery Dial', maybe it is an attribute as opposed to a model?
I can't tell for sure if this watch is yellow or white gold...
Here is a 1963 ad: Beau Brummel AAAW (ref# 04743), this variant is for yellow gold. The $175 BBBW (ref#04744) could be the white gold version, but nothing confirming that.

I'm thinking it is a BB, with 'Mystery Dial' as per the above advert.
I don't know if the OP is still active, but I also see two colours in the pics. Any clarification, Jared?
I think this watch is a 30 Jewel Beau. Case, face and jewel count match. Look at Ken's ad above; the "mystery" floating hour disc is evident and pointing at the 8.
1960 Beau Brummel
In reply to I think this watch is a 30 by neetstuf-4-u
Should this one be re-opened for re-name?
1960 Beau Brummel gets my vote.