Would it be feasible to add a Pause Queue feature?

[Rongway]

So basically if I pause in #10, I pause in #10, and everyone advances around me?
Person in #11 jumps to #9 while #10 is paused?

No.

Did you even look at the timeline diagram? Nobody starts skipping around you except to become #1 while you're paused. Everyone advances normally, including the paused people, except that paused people cannot advance to #1.

1    2    3    4    5    6    7    8    9   10   11   12
I    C    J    K    L    M    N    O    P    Q    R    S
    !!                            !!
    
[I is served.  C is paused, so holds at 2.  J skips ahead.
 O is paused but not on deck, so P does not skip them]
 
1    2    3    4    5    6    7    8    9   10   11   12
J    C    K    L    M    N    O    P    Q    R    S    T
    !!                       !!
    
[C unpauses queue]

1    2    3    4    5    6    7    8    9   10   11   12
J    C    K    L    M    N    O    P    Q    R    S    T
                             !!

[J is served]

1    2    3    4    5    6    7    8    9   10   11   12
C    K    L    M    N    O    P    Q    R    S    T    U
                        !!

From a programming standpoint, it would have to be something like:

2- You are automatically shuffled back in the queue whenever someone with your role is "behind you"

What? Why would you think that is necessary?

The coding concept is simple.

Pseudocode:

q.pop
i = 0
while q[i].ispaused
    ++i
remove q[i] and re-insert them at front of queue

Whenever the first person in the queue is served, skip anyone at the front of the queue who is paused. The first unpaused person becomes the front of the queue.