When I click on my iMac Desktop my icons disappear when I click again on my desktop they come back.

You posted in the Ventura forum, but I am thinking that you are running Sonoma.

Go to System Settings->Desktop & Dock, and under "Desktop & Stage Manager", there is a popup:

"click wallpaper to reveal desktop". By default, it is set to "always". Change it to "Only in Stage Manager" and turn Stage Manager off.

Are you referring to the dock icons or icons on your desktop itself. Check out the settings under Desktop and dock, I disabled automatically hide and show dock. I also set never to automatically hide and show menu bar. It may not be what you want but it is my preferences. Let us know if you have a different issue.

I have had my icons disappear due to a secondary display, basically the icons only appear on one screen but not the other. However I don't think a click switches between one display and another, I will check.

Yeah, this was driving me crazy too! I finally figured it out. Go to System Settings> Desktop & Dock then scroll down to Desktop & Stage Manager and CHECK the box "In Stage Manager" and BOOM the icon stay on the desktop like I used to be. Thankfully. Hope this helps.

Can you assist me?