for the cigarette lighter, cut one of the two leads on it. connect each of the cut leads to terminals 85 and 86 of a bosch-type relay. terminals 30 and 87 will end up being your switch contacts. since the resistance of the lighter element is much less than the relay coil, the relay coil will activate when the element is pressed in.
if you compare the power socket to the lighter socket, the lighter socket has the metal clip that grabs/holds the lighter element. the power socket usually does not.