This thread runs back years and more than a few people have asked "What is it that Kawasaki recommends for the transmission?". Well, on page 11 dieselbeef has put up a link to
www.bobistheoilman.com. His paper is very informative and comprehensive and here's (half) your answer. Under Hydrocracking (Predominately Group II) he writes the following: "Chevron commercialized this technology for fuels production in the late 1950’s. In 1969 the first hydrocracker for Base Oil Manufacturing was commercialized in Idemitsu Kosan Company’s Chiba Refinery using technology licensed by Gulf." Idemitsu is the oil that Kawasaki recommended; although they don't say exactly which ones and names of oils constantly change.
Of course Idemitsu oil isn't available everywhere. If you live in the UK, New Zealand or Australia, or on the Indian Subcontinent, Castrol is often the oil of choice, in part for historical reasons. Castrol also make one of, if not the
best oil available and getting hold of Castor based oil in the UK is a doddle, because historically it's been popular. (Spitfires ran on it, for instance). Similarly people in America often choose Amsoil because it's American and available. I'm sure you can buy Amsoil in the UK, but I never saw it sold locally to where I lived.
I've taken a photo of my '87 KX500 airbox, and it still has the original sticker on it recommending Idemitsu oil. (The KX has spent its life in Mexico and where I live we have a semi-desert environment. The bike has suffered what Foxx4Beaver calls "Mexican Modifications" - I would also call it "Mexican Malpractice" - but one thing it hasn't suffered from is corrosion, it still has nearly all the original stickers on it.)
The KX hasn't been used in years; if I were in the UK I'd choose to put Castrol oil in it, and the premix would be R40 or a more modern castor based equivalent. I see so much written by people on this subject, but very little of it is subjective. They haven't used it and just repeat what they've read or heard - a lot of it simply old wives' tales. If anyone want's to know how it performs in 2 strokes, I've used it in all mine, though not exclusively (and also mixed with other 2T oils), for well over 30 years - so just ask.
Having read through the whole of this topic I have decided that I'm going to use an ATF oil in the transmission the first time, not just to try it out, but also help to flush out the years of neglect and whatever it had in it, after which I shall switch to a gearbox/clutch saver type oil. The premix will be Shell Advance Racing M SAE 30 - a castor/synthetic combination, followed by (for comparison), Silkolene PRO KR2 Castor/Ester Synthetic 2T. Both are castor oils I've not used before. Jonnie