Back when that 336/44 model was made, the ATF was not as stringent as they are now, and they allowed the S/N to be under the lever on the Trigger Guard Plate on the lower Tang.
Later in time, the TGP was NOT considered the major part. So then the S/N was relocated to the upper tang (part of the Major Receiver)
More recently, the S/N was moved again to the LH side of the Receiver, same as the CB models. That just made sense, as many shooters wanted to mount Tang sights to ring Dingers with, and it also made the inhouse Marlin tooling common to all model lever receivers...............
If your S/N in not found on either Tang, I'd suspect maybe the TGP has been changed to convert to a straight stock?