Corey,
I'm using my '88 wiring diagrams, so YMMV.
The horn switch w/o speed control is a separate switch. The horn switch with speed control is integrated in the speed control switch. So if you have removed the speed control switch (as well as the under dash box), you will have the symptoms you've complained of.
The speed control version uses a horn relay (location unknown to me), yellow/light blue power wire into relay from fuse 16 30A (hot at all times), with a dark blue wire out to C305, a crescent shaped connector on LH side of steer column. DB wire continues to voltage supply brush on steer wheel then to horn switch. Other side of horn switch is grounded via ground brush. If you ground DB wire, horn should sound.
Regards,