Do I need to disconnect the line at the reservoir under the hood

Hello,

The cooler lines use a "quick disconnect" style fitting on both the bell housing and radiator/cooler ends. There's typically a safety clip that must be removed first. From your description though, it sounds like this clip may not have been reinstalled during a previous repair. If still in place however, simply place a screwdriver under the middle part of the clip and gently pry up to remove it. Once that's out of the way, you'll need to attach a disconnect tool to the line and then slide it up into the fitting to release the clips(see example in attached picture). While holding the tool into the fitting, gently pull the line free. See the link below for a short YouTube video demonstrating how to do this. Your fitting may look slightly different, but the removal process is the same.

https://youtu.be/k5r59jDnSUY