Making a touch sensitive switch is quite simple. All you need is an RS latch, a transistor and a relay. The RS latch can be built from two NAND gates.
In the example circuit below, we use two NAND gates, both being parts of the same integrated circuit (CD4011).
When someone touches plate 1 (which is connected between pin 1 of gate 1 and ground), the RS flip-flop is set. The resulting high output at pin 3 saturates T1 and energizes the relay. The relay is used to switch-on or off any load operating on mains or any other power supply.
When someone touches plate 2 (which is connected between pin 6 of gate 2 and ground), the RS flip-flop is reset. The resulting low output at pin 3 of gate 1 de-energizes the relay via the relay driver transistor and switches off the load. The diode across the relay coil protects the transistor from back e.m.f induced in the relay when it de-energizes.
The circuit can be powered from a 12V power supply unit. The specifications of the relay should be selected so that it matches load current demands.