There is a semi coil spring with 2 wire fingers to return the bottom trigger to rest. How do I orient it to drop in the top trigger component? The spring is lying lose around the axle of the bottom throttle pivot. And where does it reside?

 

I think of how the spring needs to be wound/tensioned in order to work. It will probably have to be installed so there is tension on it to hold the trigger in place so you may have to turn one leg a half or full turn before putting the trigger in position. In the end you can just try different methods until it works properly. There are only so many ways it can be installed.