I've played a bunch of old Tokai's but none with a slim neck. None with a really fat neck, either. The typical Tokai LP neck is sort of "medium" just about right for me.
On my 1982 LS, the neck is not fat as a '58 but more like a '59 model but not really slim like a '60 one.
My 2006 LS have a fatter neck than the 1982 model (not a big difference but a difference).
+1 All the early 80s LS models I've played have in between 50s & 60 necks probably a bit nearer 50s than 60s. I know it's not what you asked but the newer ES models tend to have thin necks.
I have an '84 ALS60 flametop with an extremely thin neck, very 60-ish. That (and the weight 7 1/2 lbs!) are what struck me the first time I picked it up, brand new in the shop. It's quite thin at the nut and goes to a wide/flat profile at the twelfth, kind of like a 60's 335 feel. I used to like it, now I've converted to chunky necks. Never felt one as thin as this.[/u]