'66 Mystery cab

[JaggedEdge]

So I bought a what was supposed to be a 66 cab for a project. The guy I bought it from got it from someone else. Seems this cab has been floating around with no home for a while.
I am trying to figure out what it came on originally. Door jamb plate is intact and reads:
C3636J103906
Before you ask, there is NO mistake in reading this. Not an 8 instead of a 3, ect. The plate is not beat up or scratched, never been painted over.
I cannot find any decoder online that will read this. Most say its not a valid number.
Searching around I have come to believe this may have come off a larger truck like a 2 1/2 ton. The trans cover is the high hump, but has no extra holes. (could have been swapped) The cab also has no trace of clearance lights ever having been on top.
Anyone want to take a shot???

edit to add: doesn't really matter, I am using it anyway. Came with no title, but the cab I am removing has the original plate that matches the frame#. Yeah I know... don't say it! LOL