You shouldn't ever have to put the ClickMeForColours icon in the WBStartup drawer, since it's best to apply the palette before the Workbench screen opens. If you have installed FullPalette now, it should appear in your S:Startup-Sequence with this line, which should be on the next line after C:IPrefs
Run <>NIL: FPPrefs
If this is in your Startup-Sequence (which it should be if you installed FullPalette) then all you need to do is open FullPalette (from Workbench:Prefs/), open the ClickMeFor16Colours prefs file, click on each of the colours in the GUI and make sure each one says Locked (not Free), then click Save, and from now on your Workbench should open with the correct palette. Any Workbench games, applications, GUI themes or icon sets that you open on Workbench should now look as good as they can get in 16 colours.
FullPalette overrides the default Workbench palette prefs, so there's no need to delete anything, just make sure you don't have any other "ClickMeForColors" icons or anything like that in the WBStartup drawer.