At the moment, tmux lacks the GNU screen feature to choose the same session (terminal) in different panes.
What I propose is session management rethink to make it more vim-like.
As you may know, in vim different open files are managed as buffers, and buffers are not tied to specific splits (panes in tmux's terminology). You can also have different tabs in vim (windows in tmux's terminology), containing as many splits as you want, and at any time you can choose and show any buffer in any split. Unlike vim, tmux ties up a terminal to a pane, so you can't duplicate an open terminal session, and if you want to see the same session in a different window your only way is to move a whole pane. And then, if you want to bring the terminal session back in the previous window, you have to move a whole pane again. With a vim-like session management, if you'd want to see a session in a different window, you would:

1. Open that window
2. Make another empty pane (what tmux can't do at all at the moment)
3. Open a list of open sessions in that pane and choose a session.
   And then you would have the same session in two different windows in different panes.

A little investigation shows that I'm not the only user who wants this feature -- https://unix.stackexchange.com/a/105457.