That's a steering wheel off an 84'-86'. Not for an 87'. Not sure how to make it work like that maybe somebody on here has done that swap and can chime in. Imho, you need an 87'-89' steering wheel and it would work right.

 

I’ve put that wheel on my 88. It’s a bolt and go swap and the horn will work.

I assume youve Tested the contacts with a multimeter or just jumped out the two terminals to see if the horn activates?

84-86 LX non-cruise wheel. I believe that horn pad came on escorts and maybe thunderbirds/cougars too

This is the GT style horn pad. It will fit but it’s a slightly “thicker” style with faux stitching

1984 1985 1986 Ford Mustang GT Steering Wheel Horn Pad with Emblem | eBay

Here is the LX style. This one unfortunately is tan and not the correct color. Probably out of an escort

1984 1985 1986 Ford Mustang GT Steering Wheel Horn Pad With Emblem for sale online | eBay

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There’s a few others on eBay but they are either wrong color or very over priced ($200+)

 

I’d believe that’s stainable/paintable to match. Could be a WIN.