How do you identify the NEUTRAL wire on a 2 wire very old electrical cord of a goose neck lamp?

The best way to find the neutral wire on any lamp is to ring the wire out. Before there were polarized plugs and receptacles a lamp could be plugged in either way. All new lamps have polarized plugs where the neutral is connected to the shell of the lamp holder and the "hot" wire is connected to the center pin deep in the lamp socket. Back to your goose neck lamp, you will need a meter that reads resistance and use it as a continuity meter. With the lamp unplugged and the lamp's switch in the off position connect one lead of the meter to the shell of the lamp holder. Take the other lead and touch it to one of the plug cap blades. If the meter gives a reading it is that blade that is the neutral wire. If there is no reading then that blade is considered the "hot" wire. If you are changing the plug (cap) out for a new one connect the newly established neutral wire to the silver coloured screw and the newly established "hot" wire to the gold coloured screw. Now when ever and where ever the lamp is plugged into a voltage source the polarity will be correct and the lamp will be much safer to use.