If your VIN is correct, PD4104-1400 was delivered new in May of 1955
as fleet number 186 to New Mexico Transportation Company, based out of Roswell, NM.
JLV (Roadrunner Tex) will confirm when he sees this post, I believe NMT is/was a Greyhound affiliate.
As was common in those days, many company's kept their vehicles 10 years before selling them off to second-tier operators. Thus, your coach may have left the fleet after the peak summer season of 1965 or so. Up until then, NMT took good care of it, who knows about subsequent owners - missing HVAC compartment door, destination sign glass and windshield wipers, for example.
You're on your own as far as finding "in-between" owners - you'll probably have to do some sleuthing backwards from the PO.
Very cool that it hasn't been "capped" - still has the original rear window glass, for example.
Are all three pieces in good shape? If so, you're in luck, because the glass is currently made from "unobtainium", altho Doug Wotrig may still have some of the outer pieces. Oh, and that RH top front corner marker light? Trees like to eat them, so much so that if that happens to you, you're going to have to find an alternative, as that part too is long since out of production.
It's also quite unique in that this coach still has the split windows on the front door and to the left of the driver. Most have been replaced with single panes. Unique thing about these is that you can open them up for some additional fresh air flow. Another busnut (Fast Fred) had some new weatherstripping made up for these, I believe the extra sets went to Luke @ US Coach (1-888-262-2434).
Enjoy your "new" toy!
FWIW & HTH. . .