68 GTS won't stay running

Very first thing to do is try to separate into spark? / other electric or fuel?

When it dies, IMMEDIATELY check for spark. A wrench in this gearworks is that you need to use the key, not jumpering the start relay to do this, so that you bypass the coil bypass resistor. Easiest way would be to rig a spark gap out of a spark plug, or buy a spark tester.

If that checks out, pull the air filter, look down the carb throats and work the throttle. It should immediately produce a shot of fuel from the accelerator pump.

I'm playing with EFI (last fall) but best thing I did with my Dart for poor hot start/ vapor lock was to install a rear mount electric pump, use a carb isolator, and rig a vapor return system.