So earlier this spring I had an unplanned 'get-off' as I got bit by the Snake(US421) in TN. I was able to right the bike and ride it out of the ditch(with some help) and back to the campground, but the damage was done.
After reviewing all my reasonable options I've decided to rebuild my '97LT(<56K miles) and put it back on the road. It has previously been damaged in a parking lot incident that left the main faring totaled, but mechanically and structurally was fine. Over the last few years I've stripped some parts off to keep my RT and other LT on the road.
Now at this point, I've previously sold the RT, and the remaining LT has totaled main fairing, damaged guards, damaged transmission, and over 126K miles. It is also showing signs of a leaking oil pump shaft seal(from the weep hole)
I picked up another LT for mainly the painted plastic parts(and everything else), this last week I got it all stripped down and broken down to basic parts, some of which  will be used on the rebuild of the '97, and what ever I have multiples of may show up for sale(yet to be determined) and damaged items to scrap.
Today I got the '95 up on the lift, ready for tear-down and inspection of parts to save/reuse on the '97.
Tomorrow I'm going to drop a battery in the '97, set a fuel tank on it and see if it fires up after setting 6yrs. I did a test today and it does turn over so that's in my favor..
Let the resurrection begin!!

You shouldn't feel old for having a very cool motorcycle!! I proudly tell anyone who will listen that Heinz is in her fortieth year! They find it hard to believe given her appearance. It is laughable that other Beemer owners didn't know your Brick was a member of the clan. Don't the badges and branding on the engine sort of give it away? But, people don't know what they don't know. Such agreeable, rideable beasts are our Ks. Revel in their exclusivity....just for shits.

Welcome from Hamilton, Ontario. My '86 K100RT had a shade more mileage on her when purchased. The bike sat for 9 years. Ten years later the love affair continues. I stripped her down - devoid of the fairing now. Was drawn to the engine/transmission - the industrial and raw mechanical look of her. Fluids, filters, spline shaft inspection and lube and some fresh plugs and see how you like her! There are other quirks to work on but you'll find those recommendations elsewhere....like the weird little Z tube under the tank! Best of luck.

I believe the Shinkos may have a warning on the sidewalls—Not suitable for road attacking.

Fuel pump. Replace it. They are cheap enough. Check your internal hoses are in good shape and connected.