A function for which commandp returns t is an interactive function, i.e. one which calls (interactive ...) as the first thing in its body. So you can write a function like this:

(defun insert-vertbar ()
   (interactive)
   (insert "|"))

and bind it to the mouse click:

(global-set-key [S-mouse-2] #'insert-vertbar)

N.B. In my case, [S-mouse-1] was intercepted by the window manager before emacs could get to it, so I was not able to bind it to that. I had to use [S-mouse-2] instead.

A function for which commandp returns t is an interactive function, i.e. one which calls (interactive ...) as the first thing in its body. So you can write a function like this:

(defun insert-vertbar ()
   (interactive)
   (insert "|"))

and bind it to the mouse click:

(global-set-key [S-mouse-2] #'insert-vertbar)

interactive has a lot of wrinkles (which are not necessary in this case, but they can be valuable when you need to write a more complicated function): you can find out more by using your emacs's help facility: C-h f interactive, and/or looking it up in the the emacs lisp manual.

N.B. In my case, [S-mouse-1] was intercepted by the window manager before emacs could get to it, so I was not able to bind it to that. I had to use [S-mouse-2] instead.