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.
In reply to I thought you might be by JimDon5822
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