The second "trigger" as you refer to it is the forward one at the inside front of the trigger guard. This is really the magazine cut-off lever, and when moved will allow single shot fire while keeping the magazine full for emergencies.
I think the spring you are referring to is about 3/4 inch long and about 3/8 inch in diameter, with the ends of the spring pointing out from both ends. This is the spring for the magazine cut-off lever. One end goes into a small hole (about 1/16 inch diameter) that is located in the floor plate inside the trigger guard between the round forward hole in the trigger guard that the cut-off lever comes out, and the rectangular hole for the trigger. There is a similar hole in the cut-off lever that the point on the other end of the spring goes into, forcing it upwards to the normal loading and firing position.
The spring does not set at a vertical angle, but at about 45 degrees.
.