Do you want to monitor the cars or the button. There is a difference. For actual car monitoring you would be better opting for an inductive sensing circuit that monitored the presence of the vehicle and the button press. If it's just the button monitoring and the assumption that a car has passed then this is easy to incorporate. How do you plan to display the results if at all?
Some others will be along in a bit and tell you to use a micro, don't listen to them

build the circuit using discrete components it more fun and what's better a circuit board with 40 nice shiny components on or a little black blob with 8 legs in the middle of the PCB?

I know micros are taking over the world but I am resisting as long as I can.
All joking a side choose the path that best suits you, not anyone else. We can only offer advice and our opinion.
Adam