I think I have found the elusive 1939 Time King and in great condition. The Time King and the Broadcaster are listed in G-S Catalog No. 43 as taking the same crystal. We have an advertisement showing the Broadcaster with an engraved bezel. Thus, the assumption is that the plain bezel version of the same case is the Time King. Hopefully, one day an ad will be found to confirm that assumption. The ad below shows the Broadcaster with the engraved bezel. I orginally thought this was a Minute Man but this is decidedly thinner. It is 42MM L x 19MM wide Middle x 16MM wide Ends. The lugs are only 11.5MM. She is a slender one. The movement is a 7AP 17J with a shield date code. It is 10K yellow gold filled with no bezel engraving. The crystal is 29MM x 19.5M W Middle x 14MM Ends. As you can see this is a cracked crystal so I will need to find a Broadcaster crystal. I have tried to find an add referencing the Time King name but not luck. One day we will find it.
I thought you might be interested in seeing this watch next to a 1940 Minute Man. Note the Dial is longer and narrower with a much smaller lug width.

In reply to I thought you might be by JimDon5822
I always like seeing comparison shots. It is interesting to see the subtle differences in different models.
Hard to say from this advert, but could also be a Bulova Kenneth.
Here are the crystal specs, which seems shorter then your 29mm, although a match for the ends at 13.9 / 14mm

Also found the specs for the Time King which seem way off. 31.8 x 17.2

Cool watch. I'm having no luck with an ID. I have to go Unknown at present.
I think the Kenneth advert is tempting but I'd still be tenative on that ID. I do not think it's Time King or Broadcaster right now.
I did not see the Kenneth ad before but I think it is close but this one just doesn't seem as long. The thing I question is the gap below the second register and the minute track. My watch has a much bigger gap. This one is almost touching.

Panel - we seem to be drawing blank here - Unknown?
I'm going to have to go with unknown.
Yes I’m at Unknown