What do you mean by everything quits? Electrical as well? Or does it just stall but dash lights and power to the coil is still good?
If it just stalls after 10 seconds there is a good chance it's your double relay or connections to it. The fuel pump gets power during starter cranking from terminal 50 on the starter. Once the engine starts the relay switches power to the pump over to circuit 15, the ignition. If the relay fails or has a bad connection in the #15 circuit the engine will start but starve for fuel after about 10 seconds.
Remove the relay and clean all the connections then try it. After that if it's the same get a test light or meter and start testing the relay & connections as in the repair manuals.
You could also try tapping the relay with a screwdriver handle first in case it's just stuck. If that fixes it order a new relay.
jim
'71 SB(DD only 79K(now 84K miles) & '78 FI Westy (project)
PO of '65 Beetle in '69, '70 Crewcab & '70 Ghia in '77
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