I have a 87' with a j-spec turbo swap. I have Racingbeat down pipe and preseilencer. The air pump was taken out.

My que. i noticed there should be a hose on the
BAC valve but not sure what hose. Hose off the air pump?
In the picture circled.

 

If you still have it on the car...It connects to the large plastic intake duct, to the right of the BAC. The air intake which in turns connects to the intercooler.

 

I noticed when i put my finger over it my car idles better. Should i block it off or connect to the intake plastic ducting?

 

Evidently it's been sucking "dirty" air into the intake.If it's working properly eg electrical connection seems to be on, disconnect to see if idle drops. If it does just go ahead and hook it up providing connection is on the air intake. If its been blocked off, and you don't want the BAC, remove it. If your running a/c, p/s etc, the idle may falter under a load if it's removed, or disconnected.