1980 KZ1300 cutting out problem

I'm recommissioning a KZ1300 over in Hong Kong after buying it in South Africa. It starts and runs pretty well, but has this problem:

After a minute or so of riding, the engine just cuts out. Instantly - no coughing or spluttering - just cuts out.
After pulling over and switching it off and on again, it starts fine and runs fine - for another minute or so and then cuts out again. Repeat...

I notice that the oil pressure warning light is on - I think this is just a problem with the switch or the wiring, but could the issue be related to this? Was Kawasaki smart enough in 1980 to have a safety cut-out if there seemed to be no oil-pressure?

Any advice would be warmly welcomed.

Thanks,

Keith