Advanced Engineering Tech - Help plz

this is on dads ls1.. If you jump start it with another car it will start and run and show 14 volts at the alternator and 14 volts at the battery but when you disconnect the other car from it, it only shows 13 volts and it will run's intell you turn on the lights or any other power draw occurs, then it will not start back up without hooking the jumper cables back up.

have had alternator checked twice and it has tested good both times
also battery is brand new.

Check the wiring from the alternator to the battery and from the battery to the frame for the ground. The easy way to see what cable is bad is to take your jumper cables and hook up one end from the back of the alternator positive to the battery check the voltage should be around 13.9v dc. If not then unhook the cable and hook it up to the engine block and to the battery negative. If still not working redo the test with a known good battery. If it still doesn't work then check the rest of the wiring going to the voltage regulator on the alternator. Hope this helps.