WeWire has a good point on the red leg. Then put a load on the black leg beyond the failure (60w lamp) and look for the voltage drop. It will be the hot wirenut. A noncontact thermometer is great for things like this and now days the discount tool places have them for $30 or so. They are not a lab grade instrument but you can tell the difference between a good connection and a bad one. Real handy looking at breaker lugs in a panel.
