You just identified the possible problem...a Grant Wheel. There was one on my 65 convertible when I first bought it and I had a few of the problems that you described, including the horn button popping off and landing in my while driving.

Grant does make a rebuild kit for their wheels. I rebuilt mine, but was still not happy with things (turn signal cancel, noisy contacts, occasional sparks, etc.) and decided to go back to an "original" Mustang wheel. The Grant wood wheel does look nice, but I got tired of dealing with all its little issues.
Good luck with yours!
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1965 Convertible 200 I-6, C-4 Auto (originally 3-speed manual) "Groovy Red" (originally Wimbleton White, then dark green) Newly restored and finally home!
1969 Mach 1 351 (W) 3-Speed Manual, Winter Blue, Deluxe Interior, All original, per Marti Report/Eminger Invoice. Finally moving her from the barn to the garage to begin work!