Please help me with my push button Dilemma??

I am good with most electronic basics. This has had me stumped however for a couple weeks now. I am currently using a dpdt switch to switch off my fuel pump on my car and power a solenoid. Then the reverse, turn off solenoid turn on fuel pump. My new fuel gauge has a push button built-in on it, as well as a buzzer. The button and the buzzer have there own two separate wires. I was wanting to get rid of the dpdt switch and just use the the push button. So when I push the button once quickly it beeps twice then turns off the fuel pump then turns on the solenoid instantly. Then when I push it again it beeps once then turns off solenoid then turns on fuel pump.

I already know I am going to need a couple relays but what stumps me is how to get the push button to act like a switch, with the beeping.

Any help will be much appreciated and I thank you in advance.

sorry its ment to say, the push button has 2 wires and the buzzer has its own 2 wires