On the accessory vacuum line, I noticed that there are two vacuum lines. One line is going to the L spaped connector and there is another thin line coming out of that L shaped connector. I am trying to identify the thin vacuum line. Any one know what it is and where it is supossed to be connected?

I replaced some vacuum hoses and pulled this one out by accident and can't find where it should go. I though that this thin vacuum hose goes somewhere behind the brake booster/master cylinder but it could have been tucked away and never attached to anything.

Thank you for any suggestions

1992 Pontiac Bonneville SE, L27

there is a Vac Diagram on the rad support that tells you where they all go

There is a vacuum reservoir in the area you described. It sits beside the brake booster on the firewall and looks kinda like a notched box. On my car, the vac connection is on the bottom of this plastic reservoir and is kind of hard to see. This is the vacuum reserve for your air ducts in the heater system. If the ducts aren't working properly, you will know that is the missing line. The small line going to the LF of the car feeds the cruise control vacuum motor.

Just to the left of the booster in the picture below: