Tracing a wiring fault lead me to remove all the rear bodywork for a general cleanup and a general "get to know" mission as this bike is new to me. 
I did discover how badly deteriorated the paint is on the rear frame and a forum search has turned this up to be a typical problem.
Question - how do you guys clean all the old flaking paint and surface rust out of all those VERY fiddly wee spots behind all the lugs welded onto the frame? Cleaning up 95% of it is straight forward but some advice on the tricky spots would be appreciated. 
Thinking I might go for a full frame removal and respray as I hate doing things twice. If I go this route is it worth considering media blasting and powder coating? My initial thoughts are if I can prep it well enough I will use Hammerlite satin in a rattle can. 
The rest of the frame is very good with general marks from zip ties and general abrasion over the years. The paint is still original. The bike is mechanically excellent and cosmetically nice, but I like the rides that I keep to be pristine. And this one's a keeper for sure.

I do frames with heat (gas flame unit) and a wire brush, in the difficult places theres a little wire brush with the wire pointing along the line of the bit, Stick the bit in the drill and poke it into those spots, once its been cooked by the burner it comes off easily enough

Excellent, thanks very much. I will give that a go

Rattlecan Hammerite will almost certainly leave a layer that is too thin. A good thick layer of brush-painted Hammerite lasted me two years and 30,000 miles before I had to redo it again. If you're going for the full strip, I'd go for powdercoat.

I've never been a fan of 'paint-on-rust' products.

Remove as much rust as you can. Rub back with steel wool and treat with a rust converter. Phosphoric acid products seem to work well. Make sure the work is dry first.

Undercoat and then 2 or 3 coats of a quality spray can acrylic.

Dai wrote:Rattlecan Hammerite will almost certainly leave a layer that is too thin. A good thick layer of brush-painted Hammerite lasted me two years and 30,000 miles before I had to redo it again. If you're going for the full strip, I'd go for powdercoat.

I used this to repair battery acid damage, in Satin Black and it has lasted extremely well as my K lives outside and is used in all weathers. I did sand down to bare bright shiny metal and it gave a very good finish after two coats.. Preparation is key though, if you want it to do the business.

Thank you all for your suggestions. I think I will remove the frame and then make a call on which way to go. Get some pricing etc and then make a decision. I am in no hurry as it is not my daily ride but a restoration of a bike that belonged to a good mate.

For a restoration removal of the frame is the way to go.

I used the Hammerite for repairs where pain had come off and did sand it back to the metal. I was very happy with the finish but you would not get at the difficult to reach places without a frame removal.

So the frame has parted company with the motor and is now sitting on the garage floor. The surface rust while most evident at the rear has made its presence felt in many small places over the rest of the frame. Media blasting and a coat of powder is the obvious way to go now as I do not want to do this again. I hate doing things twice. 
Can someone advise how I remove the steering lock from the frame neck? I have had a boys look through Haynes and can't see anything...
What are members thoughts on the following while I have the bike in bits. The engine has 52,000 miles on it. 
1  fuel tank to fuel rail lines. Have these a history of failure? 
2  Are there any known issues with air leaking under the intake stubs?
3  Crankcase breather hose. Do these perish as they do on K1200 bricks?
4  The timing cover is leaking near the bottom of the hall sensor cover and
    assuming this is due to poor workmanship in reassembly last time...
5  Cam chain will be inspected but what of the guide rail/tensioner blade? Do  
    these last for ever as they do on the 1200 engines? 
If there is anything that should/must be checked and/or replaced I would be grateful if members could let me know.
Thanks very much for your help

You got all then fairly right.

I wouldn't want to get it all back together (nicely painted, looking beautiful) and have it start to sound rattly after a few short months. Hence I would be torn between pulling the output shaft and chancing it...
I would go on the Forum and hope that somebody would motivate me to ensure it is working as designed as that has always been more important to me than having them look the way they were intended to look.

Thanks Rawdonball for your suggestions however this is an extremely well sorted bike mechanically. I helped with a tear down of the clutch and transmission 12 months ago to replace the engine output seal and O-ring, all transmission input and output seals, sprag service and clutch check. The starter motor was serviced and cleaned, and the alternator checked for wear, and splines lubed. The previous owner had owned the bike for 24 years and had been very thorough in keeping the servicing up to date although unfortunately he did not keep any records which is disappointing. He was a good mate who unfortunately succumbed to cancer a few weeks ago...

What was the original paint gloss level on 1987 era K's The frame did appear to be gloss but 28 years later with a few touch ups here and there with a brush, so it's a bit hard to work it out. Given the improvements in coatings now days, can anyone advise what powder coating gives the best representation of the oem look. Gloss of satin? 
Thanks for your advice