If a Paladin character was created before 1.69, even though they are just a copy, there is a bug. Phoenix's suggestion to delete override BAK, and empty the override folder works temporarily. It appears that the permanent fix is to delevel the character to 4th level, and retake 5th level, which is when Summon Mount applies. I still have to test whether this is truly fixed on Iolite, Paladin of Wilencesor, by putting my override items back in that folder. (After a couple of resets, Iolite had Mount Actions, but no Summon Mount. Fortunately, she was only 6th level, so deleveling was not super painful.

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I will now work on Honor Stillfire, who is level 17.

She has Summon Mount and Mount Actions while the override folder is empty. But she is still spawning as a horse, or stuck inside a horse. Never log out while mounted!

(I am pretty sure that Honor was created after 1.69.)
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I put everything back into the override folder, both paladins have no Mount Actions or Summon Mount.

I am now going to create a new paladin, which should work. *sigh* If this does, I am going to need to delete Iolite and Honor, and start from scratch, if I want them to have horses, plus have all of my nifty extra graphics files. *sniffle*