Hard to find much information on the subject, there is a picture of the service in action dated October 1956. Maybe it did end in 1962?
https://www.flickr.com/photos/28083...-2aJMEoL-29GG3io-VWo6rx-dFmaMt-2bdV8DA-Sn6wZG
I've been intrigued by this train too, for the reasons already articulated - not shown in public timetables (I checked several other year's issues through the 1950s, including from before electrification, when Glossop's steam services were more sporadic and some worked by a 2-coach push-pull shuttle between Glossop and Dinting. No clues in any of those.
The photographer seems to have assiduously recorded details of the train, so presumably he knew what he was talking about and it really was heading for Woodley, and not some residual peak-hour steam working to/from Manchester amongst the Class 506s.
Woodley certainly is an odd final destination. I wondered whether there had been something like a World War 2 Royal Ordnance Factory in the vicinity, which might merit an unadvertised workers' train (like the ROFs at Chorley and Risley). It seems not - or it was extremely secret!
Since the picture was taken post-electrification, Mottram Yard would've been in operation. I know the staff halt at Mottram Yard had unadvertised staff trains (Class 506 EMUs) running hourly all through the night to & from Guide Bridge and Manchester. Maybe at certain times of day there was a smattering of demand for a train for railway staff in the Apethorne Jn direction (or the union managed to negotiate one, given Mottram Yard was in a not-all-that-accessible spot)? It would make sense to start or terminate such a train at Glossop, rather than faff about reversing it on the main Woodhead line.
As
@Sir Felix Pole says, you'd really expect such a train to continue to Stockport Tiviot Dale, or maybe to Romiley and one of the Marple stations, and not 'run out of steam' at Woodley.
Without a Working Timetable from that era, I guess we can speculate, but won't know.