How to switch to the previous pane by any shortcut in tmux?

Copied from @lyuboslav-kanev

prefix + ; worked perfectly for me.

prefix + l switch to last window
prefix + L switch to last session

In tmux manual ($man tmux) you can find this section:

select-pane [-DdeLlRU] [-t target-pane]
    (alias: selectp)

    Make pane target-pane the active pane in window target-window.   
    If one of -D, -L, -R, or -U is used, respectively the pane below,
    to the left, to the right, or above the target pane is used.  -l
    is the same as using the last-pane command.  -e enables or -d
    disables input to the pane.

So, I think what you want is to use the '-l' flag, which is for switch to last pane. I don't know if there is a default key mapping defined to this task, but you can accomplish this by doing your own bindings. Something like this:

bind -r <your key> select-pane -l