You just need a timer circuit
http://www.next.gr/light-laser-led/l...EDs-l8180.html
http://circuitdiagramwiring.com/60-s...lay-timer-kit/
Those two are from a quick search on bing. You might be able to find something better but the idea is the same. I doubt a momentary switch will last to 60 seconds which is why I suggest a timer. You may not need 60 second though. If you tie it into the run position on the ignition switch, then you could possibly go with a 10-15 second switch or timer. You'd need to have your seat belt on before starting the car. The timer would start once the car has started and the key has returned to the run position.