Here's some things I would try:

1) Remove and inspect the vacuum line from end to end for cracks, splits, anything that would allow the vacuum to leak. You'll need to take off the slinky wrap to look at it closely.

2)If the ends are split or cracked, you may be able to cut off the bad part and reattach the remainder. Sometimes this is all it takes, but the downside is that you end up with the same crappy stock hose.

3) For a whopping $1 or less, you can go to an auto parts store and buy a foot of thicker quality vacuum line that will work as well and last longer.  You should also splurge and get good clips for the ends as well.  Either measure the  ID of the line or take it with you and they can match it for you.

4) With the engine OFF, test the petc0ck by grabbing a very clean container and put the fuel line into it. Turn it to PRI and it should flow. Turn it to ON or RES and it should stop very quickly once the line drains. If the fuel does not switch on with PRI or off when you go to RES or ON, then your petc0ck is not working right.  You'll need to remove it and inspect  it.

5) If the petcock functions normally with the engine off, reattach the fuel line, recheck your vacuum line clamps and go for a short ride. If it still cuts off on you then your next place to look would be the carb float.  

6) They're all pretty quick checks but any one of them can bite you.

I wouldn't rule out the possibility of a wet or faulty spark plug wire.  It is worth inspecting it. If he finds he has good fuel flow from the petc0ck, a carb float that works properly, a clean air filter, and proper idle speed then intermittent spark could be the next culprit.