Wanted to find out if the fuel pump for an ap1 2001 model runs continous once the ignition key is turned on?

 

Yes

 

It should run for two seconds to prime the fuel system when the ignition switch is turned to the "ON" position then turn off.

It will turn on again when the start button is pressed and will run continously when the ECU senses engine rotation (ie. engine running).

 

My car once the ignition switch is turned on the pump remains running whether I start the car in 1min or 5mins later

 

Has this been this way since you bought the car or did it just start doing this recently?

If its been that way since you bought the car, I would check the wiring on the connector that goes to the top of the fuel pump assembly. Previous owner could have rewired that connector for direct power from the battery for an aftermarket pump and could have mucked it up.

 

Does the car have an aftermarket ECU?

 

Yes bro it came with a spoon computer and it has always been that way. I thinks it's a wiring issue as mentioned by cool guy

 

It is common practice on forced induction S2000's to run a direct battery power wire back to the fuel pump and use a relay right at the pump to get higher voltage to the pump. This requires cutting and splicing of the wiring at the top of the pump assembly (or de-pinning of the wires from the connector). You may be able to see signs of tampering if you take out the three self-tapping screws that hold the pump cavity cover on and lift that cover up to look down at the connector that sits on top of the fuel pump assembly. Check all the wires that run to that connector for any splices or electrical tape, etc.