What should I consider an E-6 who takes an excess E-4 slot for a deployment?

During Desert Storm, I was assigned to lead patrols on the perimeter of our camp due to previous training and experience. I was an E-5, yet would sometimes get E-6, and even E-7, personnel detailed to me. I respected their rank, of course, but they always let the rest of the patrol know that I was in charge, and that they would obey any lawful orders I gave. This is exactly how your E-6 should be acting. Good leaders are good followers, too.
I would suggest that you bring the matter up to your actual chain of command, as his behavior is likely causing disruptions to the work flow, as well as creating friction in the unit. I wouldn't confront him directly about it, if I were you, as it could lead to more problems.
Personally, if I were filling an E-4 slot as an E-6, I would enjoy the vacation from the normal responsibilities of a staff NCO and just do my job and chill.

A SSG is a SSG is a SSG. So yes you consider them a SSG. I put a 12C SSG in the S1 for a time because the section lacked discipline and we were short, the admin SGT was technically savvy and did well at the Admin tasks but was overwhelmed by the additional leadership tasks required to run the shop (normally an SFC).

What I noticed with our NG round out unit in 03 was that in some cases the "go to guy " wasn't the guy with the most stripes and that the unit took folks from all over to bring it up to strength and folks were working in MOSs and slotted in grades that they hadn't been in, in years just to fill the unit. They did a great job for us but it took a minute to figure out who was who.

Point is; regardless where the SSG is slotted on the MTOE if they have the MOS as a secondary or third the Commander and 1SG can utilize them where they need them. Even if they don't have the MOS but there is a need that they best fill they can go where the Commander and 1SG need them.

What duty position is the E6 in? If he is in an 11B slot he needs to stay in his lane.