Relay to control the power rail on a PCI adapter
A solid state relay rated for mains voltage will use a triac internally, so it will drop 2V, won't work for your 12V application. Also it is likely not to turn on at all.

Just use a PMOS as a high side switch. Pick a PMOS with proper RdsON rating according to your current for low voltage drop, and GND needs to be connected on both sides of course. Schematic example:



Or you can use a high side switch like this one.