Tmux keybinding to swap pane left or right
:bind-key -n C-{ select-pane -L \; swap-pane -s '!'
This should tell tmux to select the left pane, and then swap with the previously active pane.
Also, swap-pane -s {right-of}
seems to work.
Here is the list of ways to refer to other panes:
{last} ! The last (previously active) pane
{next} + The next pane by number
{previous} - The previous pane by number
{top} The top pane
{bottom} The bottom pane
{left} The leftmost pane
{right} The rightmost pane
{top-left} The top-left pane
{top-right} The top-right pane
{bottom-left} The bottom-left pane
{bottom-right} The bottom-right pane
{up-of} The pane above the active pane
{down-of} The pane below the active pane
{left-of} The pane to the left of the active pane
{right-of} The pane to the right of the active pane
See the online man page for reference.