Is there an AR stating that a Specialist has to go to parade rest for a Specialist?

They should go back to making specialist who are team leaders corporals.

Yeah, if that ever happens to me, I am finding the nearest NCO who knows me and having said Specialist participate copious corrective training. I address COLs for LTs and advise CPTs on what needs to be done to ensure their company is mission capable because of my expertise. I would never dream of even asking someone to stand at parade rest for me. Even on my JNN team. Regardless of position these are my peers and outside of my duty to run my JNN and train them, I treat them as such. Maybe you can do it by regulation or virtue of position but a true leader is humble and that is not showing humility.

I ran into a situation somewhat similar to this back in 2008. I had just been placed as Team Leader and had another SPC and a fresh out of basic Private under me. The other SPC and myself had talked and came to the conclusion that we would treat each other as equals and that any corrective action that needed to be done would involve the squad leader until I received my Corporal stripes.

I think the position is important enough to respect their wishes. I was a team leader in the infantry as a specialist before I commissioned. Now that I'm in MEDCOM I see company commanders as captains with entire hospital departments in their company. Department chiefs at my hospital are usually COLs. You just gotta be professional about the position. especially in front of their joes.

There is no regulation however, if they are slotted by TDA, and duty positions in an E-5 slot then yes you must stand at parade rest and address them as such. Duty position, time in grade and service are covered in the refs.

Ar 6-22 army leadership

No

No you don't and its not written in any reg, that SPC should be laterally promoted to Corporal to prevent that kind of issue

By the fact that the SPC is a team leader he does have the authority that his position is entitled to. Many years ago I was assigned to an Infantry unit that was being re-organized into a Stryker unit. As a Tanker I had very little contact with Corporals (not really a rank given in the Tank world). As a Sergeant I outranked all of the non E-5 team leaders. At one point I was cross attached to an infantry platoon because my platoon had too many E-5's then MTOE allowed. I was slotted in with a fire team that had a corporal team leader. the Squad SGT (an E-6) made it known that I was answerable to him alone, but when it came down to it I would do as my team leader instructed within reason. I had a great working relationship with this Corporal and learned from him as much as he learned from me. In that situation the boundries were set out on what was expected. If that team leader instructed me to perform a specific action as long as it related to my specific duties as a rifleman then he was in the right. At the same time I could not just ignore his instructions because I outranked him. It was a lot of give and take. I suggest that if you believe that there is a problem or situation talk to the next higher in your CoC ; Most likely your Squad Leader. Have your team leader present and make your thoughts known.

Not sure what goes on in the Army, but in the Navy petty officers regardless of grade acted like colleagues, and called each other by first names. We would regard a demand for "address me by my rank" as an indication that a person had lost their mind.