Driving 60v switch with 3.3v (800ma max)?
Something like this circuit may work for you:



You would replace your switch with a relay of equivalent specifications. Digikey has a few relays with a 60V coil voltage.

The circuit works as follows:
When the control signal is applied, the N-channel MOSFET turns on, which allows current to flow from the positive battery terminal, through the coil, thus turning the relay on. When the control signal is removed, the 10k resistor pulls the gate back to ground, thus turning the MOSFET off, and the relay as well.

The diode stops the inductive kick of the relay coil from destroying the MOSFET when the circuit turns off, and the 100 ohm gate resistor is just good practice, the circuit would work fine without it. 

One thing to watch for is that the MOSFET you select must be "logic level" meaning low voltages like 3.3V are enough to turn it on fully. Also be sure to choose a MOSFET with a high enough voltage and current setting for the relay of your choice.