Hello Cam
Engine wise, consumable parts for a 1979 Briggs motor are easily available, chassis wise it would mostly amount to blades, wheel bearings, bushings and axle clips still being available.
Vulcan was made by Jetfast/Supaswift in case you haven't found that out already.
Provided it runs alright without smoke, it would probably only need a few things. If it won't start cold like it used to, there is an issue with the choke, which is controlled by the carburettor diaphram. GA spares CAM506 is the part you need.
NOTE - when you pull the carburettor apart, there may be a dowel pin in the middle with a microscopic teflon washer (usually stuck to the old diaphragm). This is a factor repair to fix a common fault. Do not lose the washer - they are not easy to find.
Do 2-4 oil changes in relatively quick succession to help clean out the motor. New plug (br2lm ngk) and air filler and all that.
Being 1979, it will probably have ignition points. You can put a new coil on with magnetron which will bypass the points. But a new coil is $85. I would suggest scrounging a coil off of a newer briggs (any one labeled classic, quattro, sprint made up to 2012 - not quantum) and throwing that on
