Hard start when warm? Smoke?

My stang is still suffering from hard start issues after doing some basic tune up work. So far I've replace all plugs/wires/cap and rotor as well as replaced a vacuum hose which goes from the side of the Cobra intake into a black box in the front passenger side (?). I thought that was the culprit due to a serious chunk of hose missing caused by my headers, but the problem is still serious.

First start of the day is normal, car runs well, if I then park from an hour or more and restart the car it barely turns over. 5-6 seconds of ignition and help from the gas pedel will start it, but it aint pretty. After the startup I get a large searching Idle, which stabilizes, a puff of white smoke, and the smell of gas.

Car still drives fine once its on.

Can someone check the top of that black box I mentioned, as of right now I have one hole pugged with a black cap, and the other is open. I'm wondering if I pulled on the vacuum hose to the point where it unplugged near there??

Thanks for the help guys

What does the cap look like that covers the second hope on top of the box?

Is it just a cap which plugs it, or is it a part??

What would be the effects of a car running without that cap in place, could that be the reason for these hard starts???????