If the oil light is coming on when idling, you have issues.
Check the oil level. What is the type and grade of oil? Was the filter renewed?
With regards to the alternator, the "trickle supply" RC speaks of, is the small wire, that leads to a light on the dash. If its broken it won't highlight a fault, and will cause charging problems. I'd have thought if the battery light comes on though, it wouldn't be that thats at fault?
When runing , stick a multimeter over the battery terminals....do you measure approx 11-12V or closer to 14V???
When it does cut out, battery and oil lights coming on are normal due to the stall...thats not an issue....but oil pressure at idle is a problem.
As mentioned though, the oil pressure sensor circuit is grounded through the block, so it may still be a ground issue.
Cheers,
Kristian