Hello Simon,
Thats a very nice bike you have there, if I was riding that I'd have a big silly grin all over my face every time I got on it.
As far as identification goes, Peter C who appears here can give precise detail. I'm not that much of a Triumph man myself, nor have I worked on that precise Triumph oil pump set up but they are all the same in general principle Imagine a bicycle pump with a simple non-return valve, a little spring loaded ball springs to mind plus possibly some sort of anti-siphoning device also.
I have the Villiers Autolube system on my Radco and its anti siphoning device consists entirely of an air leak at the right place. A little pinhole which if blocked allows all the oil to siphon from the oil tank directly into the crankcase as has happened with the Triumph. Idiot simple but very worrying the first time it happens to you.
My feeling is the Triumph survival rate is so high you will quickly meet other other owners of this model who will give you all the tips and tricks necessary for pain free riding.
Lastly, you are making me envious with your question about what oil to use in the primary chain case. The vintage Triumph was a quality bike. My bikes are rather more downmarket and none of them have the luxury of a primary chain case. A guard to prevent muck getting everywhere is the best mine have. As it is I generally have a well oiled left boot. I can only dream of a nice clean properly oiled primary chain and a clean boot.
Cheers, Bob