The T/C Renegade and Hawkin double triggers are the same. ie: the two trigger set's should look the same and are in fact interchangable.
If your new purchase dosen't work, I'm guessing someone "customized" it. I really don't know what you mean by "plunger lever".
For clarification the trigger has two trigger
levers; the part that raises, front and rear.
They (one or the other) engage the part of the
lock called the
trigger sear.
I'm not trying to be a smarty pants here, I'm just trying to figger out what part you mean??