Good news………. or bad news? Whatchu want first???
Good news is it does appear to be of the vintage you guessed. It also appears to have it’s original pins (tumblers, the part that interacts with the key’s cuts). Yale’s original (nickle-silver) early pins had the striations as can be seen in your photos.
Other than that there isn’t much light that can be shed as to the desk itself, as Yale made gazillions of desk locks for a myriad of cabinet & desk manufacturers.
The stampings on the face of the lock are the code which can (by a well skilled locksmith) be decyphered to generate you a working key, if you do not have one for the lock.
The “1309” is the code itself, it is associated with there being 4 pins in the lock. The “JA” is the key profile (shape of the key’s millings) The “R” is either a prefix key number by the furniture manufacturer (Yale designated) or maybe, and I must state MAYBE the cabinet/desk manufacturer’s initial.
Hope some of this makes sense,
–Vince
PS. I assume you visually scoured all nook & cranny surfaces of the furniture? IE: under/inside each drawer/opening. You’ll be surprised what may be stamped/burned/glued. Name of builder or city is VERY common on old furniture.
