The manuals you seek are...
from Cylmer part number M383 "Suzuki GSX-R 750-1100/'86-87 & Katana 600 '88-93" the ISBN is 0-89287-590-9
or from Suzuki part number 99500-37033-03E "Suzuki GSX-R 750 Service Manual"
As you're in the UK the interpretation of the VIN may be different, but if you think it cam from the US it might confirm that belief. Here, and maybe other countries too, the VIL has some info in it.
My VIN for instance, and I'll but a # where a digit should go because I can be paranoid at times, is found imprinted on the head column and on a finished plate a couple of centimeters away on the right side of the bike.
My VIN is...JS1GR75A-0G#######
I don't know of any identification system that is used for the motors.
My motor # is R705-126950
There appears to be no relationship or similarities beween the two numbers.
Back to the country ID I spoke of earlier.
1. Country J: Japan
2. Make S: Suzuki
3. Vehicle Type 1: Motorcycle
4. Safety equipment G:
5. Line R:
6. Price Class 7:
7. Body 5:
8. Engine
9. Check Digits 1,2,3,4,5,6,7,8,9,X (Check digit is a single number or letter used to verify VIN accuracy
10. Model Year G:1986 F:1986 H:1987 etc...
11. Production Plant ?
12. Serial Number 000001 to 999999
Other bikes I've owned have had their VIN's begin with...
JH (Honda)
JK (Kawasaki)
The finsished plate on the right side of the bike should also have a date of manufacture stamped into it...mine is 3/86
Hope it clears up your questions.