So, my bike is a project. P.o. never rode it, except once down a long gravel road, mashing the rear brake all the way. That was in 2006, I think. I don't think it's been started in 5 years.

I'd like to rescue it. Last Sunday I got the fuel tank cleared out. Have ordered a new battery, and might get a new air filter, just because. Dug into the front brakes today...

I'm trying to append a pic of the wholly gunked up MC but we'll see how that goes...
See how the piston is mired in place!

Forget the air filter replacement.  Just clean the old one and put it back.  You'll need to save your pennies for other items that need replacing.  How's the condition of the Z-tube for instance?

Welcome! How many miles on the clock? If it were mine, I'd like to see at least 40K. Idleness is the K bike's worst enemy.

Fuel degradation is the biggest problem. followed by perishing rubber stuff. Get the injectors out and clean them. It may take a week or so of soaking to get them working, or sending them off to a service that cleans them. Fuel lines and the previously mentioned Z-tube should be changed. If they don't leak right now, they will in the near future.

Get into the drive shaft splines to see what they look like. If you need to replace the shaft or the final drive you want to do it when you can spend a while shopping for good used parts.

As you work on your bike, you will find that eBay is your friend. There are lots of used parts there with a wide range of prices and conditions. The large number of K bikes being hacked into cafe racers is resulting in a lot of fairings, seats, handlebars, and instrument clusters coming up for sale. There are also many bike breakers parting bikes out there as well.

Robmack and .75, thanks for responding! The guidance is much appreciated!!

The bike has 12k on the odo, but I don't know whether it's an accurate instrument or not, or even hooked up...

I do know this bike has sat overlong. I have no clue yet about the fuel system, but bet you're right that it'll want a total rebuild.

Got a copy of a major job by Motospezial in Alberta, but doesn't look like much driveline work was done. Don't know about the splines yet...

It might have 12,000 miles, or it's also possible that the odometer has stopped working, a lot of early ones have bad gears in the odometer drive.

With low miles, there is a pretty good chance the fuel has varnished everything up. There is lots of information on YouTube on cleaning them. It's also a possible to have them cleaned professionally. There is also a good chance that the rings are stuck in the pistons and need to be freed up. A compression test will tell you if they are working properly. If they are stuck, you can put a little shot of Marvel Mystery Oil in the cylinders and crank the engine over for a few seconds with the plugs out to spread the oil around. I would do this every day for a week or so while I'm working on other stuff.

As far as the air cleaner, I would figure that it's still in almost new shape, but that there is a good chance that at least one family of mice or chipmunks has made a home in the air box at one time or another.