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So far, only the light blue Infantry braid is authorized on the right shoulder.
The French fourragere is authorized to wear on the left shoulder for some units, like the 82nd.
Shoulder braids for non infantry are often only authorized for those who are given permission, like a color guard volunteer.
Infantry is currently the only authorized cord. However, a few units will allow non infantry personnel to wear their unique cords (red for artillery, gold for cavalry, etc)
IF they are ASSIGNED to an infantry unit.
Therefore, it looks like the only way you can wear that crimson and yellow ordinance shoulder cord is if:
1. You volunteer for the Honor Guard or Color Guard in your unit.
2. You are assigned to an Infantry company that allows non 11 series MOS's to wear their cords so the entire unit wears a cord.
If you want to spice up your uniform, go to Jump School, and request the 82nd Airborne at Fort Bragg. Your beret will be maroon, you will wear jump boots with your class A uniform with your pants tucked inside the boots, your jump wings will have your battalion's colors behind it, and you will wear the green and red French Fourragere shoulder cord.
The Army shoulder cords for each MOS were an experiment back in the 1970s.
AR 670-1 Wear and Appearance of Army Uniforms and Insignia