The zenity --notification do not give simple interaction possibilities.

Can be very useful if a left mouse click on the icon calls some command.
Will be very useful too if a right mouse click opens a context menu.


Setting event handle proposal:
zenity --notification --onclick="<some sh code>"

Example:
zenity --notification --onclick="zenity --info --text='You click me!'"

This will call a external program and can be good fo the most things
what i think, but if we need to call a interna function we can do this:

trap internalFunction 50
function internalFunction() {
  zenity --info --text="You click me!"
}
zenity --notification --onclick="kill -s 50 $$"


Setting a context menu proposal:
must be added and can be modified on the fly using --listen.
add-menu-item:<icon path|none>|<item name>|<some sh code>
add-menu-separator
remove-menu-item:<item name>

Example:
echo "
add-menu-item:bli.png|Say Bli!|zenity --info --text='Bli!'
add-menu-item:|open my picture|eog ~/$USER.jpg
add-menu-separator
add-menu-item:about.png|About|zenity --info --text='This is an Example'
"
zenity --notification --listen