You could use a relay with a 555 timer circuit or capacitor circuit to latch your relay for the time required.
On a normal relay you have a coil side and the Switched side. So you have 4 different connections. You could have polarized connections for the coil but not necessarily. Polarized meaning one needs to be + and the other -.
In a latched relay you ground one side of the relay and you trigger the other side with the +12 volts. To make it a latching relay you put a jumper between the switched +12 and the side you are putting +12 to on the coil. This works because once the switch is closed and providing +12 volts it will basically be turning its self on. You then break the connection by disconnecting this jumper. You can disconnect the jumper with a simple 555 timer circuit or a capacitor driven timer. If you do a google search for 555 timer you can find many simple circuits to accomplish this. Just make sure you are aware you need to do it for a +12 volt system. You might be able to find a capacitor circuit that works better. This should be a very simple and easy to build circuit.
Old Spark may chime in with the correct values and correct circuit.