It sounds like some wiring got crossed or connected wrong. On your starter relay (on the fender) there should be two wires, one is a red with a blue stripe, it should be on the S small terminal and there is another wire it goes on the I terminal (Trucks with the hot fuel handling package used that terminal).
Unplug the wire to the S terminal and see if the issue goes away, if not, then your starter relay is bad.
Bill AKA "LOBO"
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"Getting old is inevitable, growing up is optional"
Darth Vader 1986 F350 460 converted to MAF/SEFI, E4OD 12X3 1/2 rear brakes, traction loc 3:55 gear, 160 amp 3G alternator
Wife's 2011 Flex Limited
Daily Driver 2009 Flex Limited with factory tow package
Project car 1986 Chrysler LeBaron convertible 2.2L Turbo II, modified A413