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Hello Dave and thanks.
That last one first. invalid .desktop command not shown in icewm.
Not a desktop-menu factor, just a observation of curiosity.
I did not know icewm had that. xfce menu just got it in the last version update. kde, dolphin, thunar have try exec validate on their menu.(i think)
I happen to be on antiX25a the firejail and firetools not installed showing icon on jwm and fluxbox menu is where i spotted it.
Test it by going into a .desktop file and alter the Exec.
app-select.desktop open and change Exec= to /usr/local/bin/app-selectDave as the command;
run desktop-menu. app-select will not appear on the icewm Accessories menu.
jwm and fluxbox Accessories>app-select will show but not work.
version 3.33 same.
((app-select.desktop change it back to Exec /usr/local/bin/app-select. ))
Geany is an interesting test because on this system it is the sole entry in category Programming. Wreck the Geany Exec= and icewm does not show the Programming category because the only Geany entry fail try exec.