A 1946 AMERICAN EAGLE has not been IDed before. This is my candidate. Back of the case has enscribed date 12-25-46. Case is one of three types I have seen with 1946 movements that might fit the picture in the ad for 1946. The other two have lugs that inclose the corners of the crystal.
The crystal may be a replacement, the watch is 65 yrs old! While I am the same age I have only owned the watch for for a short time. Nonetheless, the case in your picture ( 1946 Director) is different in that the lugs on my candidate are solid (without a corner notch) and do not extend beyond the crystal. I have seen several examples for sale that are the same (those had different crystals as well). The full numeral set on the dial of my candidate is the same design as in the ad picture, as are the hands. The example "Excellency" watches in the myBulova data set have abbreviated sets with only every other number, or the numbers in the 1948 version are shaped differently than those my candidate. The numerals in your 1946 Director picture are shaped differently than those in my candidate.
I just reviewed the pictures of the 1940 American Eagle in myBulova and note that the dial and hands are the same as in my candidate 1946 AE. Would not have noticed but bought an American Eagle off of "that site?" yesterday and wanted to look again at what was listed here to see if I bought a good one! Will have to wait 'til it gets here by snail mail, but am encouraged, and excited! This is a bad sign, I must have been enchanted by the Bulova Goddess of Time!