Some may find this innocuous, but (first responder) ceremonial guardsmen need to maintain a professional image when in uniform before, during and after a ceremony. Any other time that we are out of uniform, dress is most likely not an issue.
For us in the military, it’s a big no-no to tuck gloves into an epaulet. That’s not where they belong (on your hands, in your left hand or put away somewhere).
When I was on the Base Honor Guard at Davis-Monthan AFB in Tuscon, AZ many years ago, my team and I had the distinct pleasure of escorting President Reagan for a visit. When we were finished, he took the time to shake each of our hands for an official picture, but what were we to do with out gloves? Our Lt made the quick command decision to have us all tuck the pair into the bottom of our ceremonial belts. When the pictures were finished, we pulled out the gloves from our belts and carried them in the left hand until we were back at our transportation where we could put them away.
What does this all mean for you? You’re organization is not the military, but you wear a uniform and are a paramilitary organization which means you also have certain standards to uphold. Sloppiness is in the eye of the beholder, but I do agree that gloves on the shoulder do not present a professional image and should not be practiced at all.
Am I able to point you in the direction of a rule that says “Do not tuck your gloves into an epaulet on your uniform after you are finished wearing them”? No, I’m not. What I suggest is for your organization to create uniform wear guidelines, an SOP (Standard Operating Procedure), if you haven’t already, that specifically addresses your concerns for the members of your unit and then stricter guidelines for the honor guard members.
Shaking hands with while wearing gloves is inappropriate and wearing them after a ceremony is not a good idea, but where can gloves go? In the uniform cover (hat), in your left hand or out of site under the blouse tucked into the uniform belt. All until everyone can get back to their transportation and put them away.