I do have to mention here that there does exist a rather rare possibility (though highly unlikely)..that your machine is a Late Series 1 to Early Series 2 transition machine, but the Series 1 to Series 2 transition ones that I have seen already have the Dataplate mounting on the rear of the bedplate, and do not have the painted Edison signature in the Rear of the Bedplate as yours does. I still think that your Amberola 50 is a Series 1 Amberola 50. All the evidence shown points in that direction. Someone has just done some parts swapping with the reproducer and the Speed Control/Governor cover...and obviously removed the Dataplate. To answer your overall initial question, All Edison Amberola 50's came with Serial Number ID "Dataplate" tags. The one for your machine would have been the 1st Series 1 Style.. Black over Aluminum.
*Below is a pic of one of the most peculiar Amberola 50 Dataplate mountings. I'm guessing that it's not factory and was done by a previous owner who did not like where it was located by the horn area originally, so he moved it to the back wall of the cover. OP (MikeB), Pay close attention to exact type of dataplate seen here as it is a Series 1 Amberola 30/50/75 Dataplate, The is the same exact design that I believe that your machine should have (or had originally-now missing).
Tony K.

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Edison Collector/Restorer
Melbourne/Florida