Re: 1980's Falcon Everest
Not much help but my K2 was mostly Shimano drivetrain components, a mix of mid range touring spec stuff and nicer Deore Deerhead parts. If you search on here you'll find some pics. The Everest would likely be lower spec but I'd still expect Shimano.
I reckoned the frame on mine was better than the kit, so I had an idea to upgrade to slightly newer SIS compatible kit - maybe Deore MT60? Depends if your peiority is getting close to original/period correct, or you just want it to ride nice.
At present yours has been "upgraded" to SIS but with entry level Shimano mech and shifter. These work well enough but Deore (or even Exage or similar) would be lighter, prettier and slicker.
But on the other hand as someone mentioned above, if it rides nice probably just as well to leave it alone!