The Service Manual Supplement points out that the Neutral Start Switch can only be properly set after the shifter linkage is properly adjusted. You need to have a "0.05 inch overtravel gap". As you have the service manual, try the linkage adjustment procedure on 7F-3 first.
PS: the correct spacer they call out for (.094") is 3/32"
2012 Mustang Boss 302 #1918, Competition Orange. FGF replacement 2006 Mustang V6 Pony, Vista Blue. Factory ordered. 2019 BMW X3 (Titled to the wife, but I'm always driving it for her. So I'm claiming it) Old projects, gone but not forgotten: 1967 FB 400, original CA car. After 22 years of work, trashed by the guy who was supposed to paint it. I had to sell it. 1980 Turbo Trans Am 1970 Mustang fastback, 351C 4Bbl, auto 1988 Mustang GT, 5 speed 1983 F-150 4x4, built 302 1994 Chevy K2500 HD 4x4, 454 TBI
