Usually I just replace power supplies

so dont know that much about the inside either but I do know that car batteries can give quite a lot of current, not sure if a PC power supply can...I can imagine PC hardware only using tiny amounts.
Maybe that's why the lights pulse because the capacitors give out burst, then recharge?
There is more to electricity then just the right voltage, maybe you should check some more specs on the neon light and the power supply. (volts, watts, amps)