You can also hookup a little thingy that takes sata power on one side and 24 pin on the other. As soon as there is power on sata side, relay switches and second PSU turns on.
This may not be fast enough for some add-in cards. It would be better to connect the PS_ON (green) cable from both ATX24 connectors together, so that the motherboard turns on both PSUs simultaneously.
This would still have the disadvantage that the PWROK (grey) cable from the second PSU would not be monitored by the motherboard, leaving the machine prone to partial reset quirks during brown-outs. Normally a motherboard will shut down when PWROK is deasserted, and refuse to come out of reset until it returns.