Can I use mouse click to focus on Byobu splits?

Yes, this is very much possible.

You simply need to turn on mouse support in your ~/.byobu/.tmux.conf configuration.

Add the following:

set -g mouse-select-pane on
set -g mouse-select-window on
set -g mouse-resize-pane on
set -g mouse-utf8 on

This will allow you to:

• select a split by clicking in it
• select a window by clicking on it in your status bar
• resize a split by grabbing the border and dragging

However, you may now find it difficult to use your mouse to click on some text, and highlight (select) it. To do this, you'll now need to use either Shift-LeftClick or Ctrl-LeftClick.

Full disclosure: I am the author and maintainer of Byobu.

In Ubuntu 16.04 this solution no longer works. It seems that config has changed in tmux new version (from tmux 2.1 and up).

Now you must copy (append) the following in your ~/.byobu/.tmux.conf file:

set -g mouse on
set -g mouse-utf8 on

for me, neither of the above solutions seemed to do anything.

Restarting the terminal session, and restarting byobu with those settings in the config file did nothing.

One magic keypress changed all that:

Ctrl+F12 and you get the message "Mouse: ON"

(Ubuntu 18.04, tmux 2.6, byobu 5.125)