What you want to do to unbind your S1 when you have it equipped on multiple characters across mutiple profile slots is:

• Step 1

Unequip the S1 by right clicking it and click the "x" icon in the upper right hand corner to close the agent profile screen before moving on to the next profile slot.

• Step 2

Repeat this step across all your profile slots on all characters.

• Step 3

Now your S1 should be unbound and it will show up when you try to mail / deposit / auction it.