It seems that this post has split into two different questions; Why is there no Lodge/Chapter Chief Position Patch and When should different shoulder loops be worn. Please allow me try and shine some light into this discussion.
The first question of "Why no Lodge/Chapter/Section Chief position patch?" was answered by the 2004 National Vice-Chief who served on the National Advancement Committee (which designates which patches get made) at a National Leadership Seminar last year. The answer is quite simple. As a youth, you wear position patches to designate your position of responsibilit