MATE desktop - changing icon of a Launcher

[Richard Owlett <rowlett@cloud85.net>]

I've been use MATE almost since it came out.
IIRC I used to use a series of mouse clicks to determine the file name 
{including path} of the current icon.

On my current systems {one Stretch, one Buster} if I:
 1. right click on the Launcher
 2. select properties
 3. left click on the current icon

I get a "Select Custom Icon" menu. In it I can select a directory to 
search and it will display a list of available icons in that directory.

But I need to know the complete path to the current icon.
I can get the desired information by opening the launcher with a text 
editor. {I want a "mouse click" method to obtain the information as I'm 
setting up a system for a very novice user.}

Suggestions?
TIA