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The above link seems to say don't do the upgrade but it shows you the relay you need to check. You can either replace with new OEM relay or upgrade with a starter type relay from a Ford.
Your problem is the 12-24 volt starter relay under the dash. It takes the 12 volt input from the ignition switch and makes it 24 volt for the starter start terminal. It is a common upgrade to put in a better relay as it is a super common problem for them to stick and eventually burn the truck...