There's a couple of things to check. First off, if your steering column has
any kind of rubber insulated "rag joint" under the hood, then there is a
little piece of metal that jumps the rubber. In the past, this joint was
prone to corrosion.  A simple way to check if this is the problem is to
remove the horn pad and grouind the end of the steering shaft. If the horn
button works after adding this ground, the cruise usually will work as well.
Of course, you then need to fix the ground permanently.

Next, check the horn relay. When you have factory installed cruise, there is
a horn relay which also provides current to the on-off switch so it can turn
the cruise module on and off.  If the solenoid in the relay is open or it's
not receiving power, then the cruise control can't initialize. Finally if
this doesn't work, pull the steering wheel and check the two brushes
contacting the race tracks under the streering wheel. It's possible one is
worn to the point it no longer contacts reliably.

Keep in mind this advice probably will not work for the airbag equipped
Mustangs of later manufacture as they lack the brushes in the column and
have a clock spring tape instead.

As far as I know, the horn relay is the only common point between these two
circuits.