You dog, free and it's one of the Good Ones!! (obviously that's humor - great machine)
I'm not home right now to check the manuals, but that should be around a mid 70's to early 80's.
You'll likely need a carb kit (most everyone does). Yours is just a smaller brother of this one:
Or this one
Things to watch - The transmission is hung from an 'intermediate' shaft. The 2 shoulder bolts that mount it to the tractor unit can come loose over time - not a good thing. Insure they're tight.
The axel and auger bushings are plastic (darn bean counters). I have a thread on how to convert it to roller bearings, check under maint heading.
Personally I don't like how the one handle controls both the auger and drive. I came up with a way to split those 2 controls but parts have to be made.
The main control cable isn't available from Sears, but it is still available. The chute cable isn't (at least I haven't found one).
If a cable end is broken, you can buy a replacement end from McMaster Carr.
Unfortunately alot of people don't maintain them properly. I've seen a number where the auger rakes are stuck to the shaft. Takes effort to get them off.
If you need to pull the auger apart, leave the impeller portion bolted to the tractor unit unless you're 1) a glutton for punishment or 2) extremely good at documenting. It's easier to pull the tranny, unbolt the auger pulley and remove it then unbolt the front section of the auger housing from the impeller portion and pull it apart that way. The part of the idler controls for the auger and drive are bolted in there and can be a bit fidgety if you mess them up. This way you don't have to touch them
That's the one I split the controls on.
Don't mess with the stator in the engine (under the flywheel) for the light unless you're willing to go through potentially retiming the engine (applies to all Tecumseh engines).
Here's one of mine (one of around 12) I've rebuilt that started similar to yours (but with a 32" auger) that I swapped down to a 26"
All the comparable 536 prefix machines are pretty much interchangable in parts (whether red & white or black & gray), the 5 hp and below vs the 7 hp and above. Virtually everything you'd need is available somewhere and that machine you have is a beast.
Let me know if you need any info (and I do have a manual that's close enough with a parts list). Just be aware in typical Sears fashion, the same part may be listed under multiple part numbers, with some listed as discontinued/unavailable while the same part may be available under another number.
Most of the ones I've bought have not had a skidpan on them, I ended up having to make them from scratch.
Hope that helps.
PS - if you want to read the thread on rebuilding that gray one, here's the link: http://restorationmen.lefora.com/201...-and-proceedi/