What you have is a poor ground. LIKELY (But not necessarly) on the rear turn signals.
Here is what is happening:
The cruise control reads the voltage across the brake light switch, It wants to see 12 volt on the high side and zero on the load side of the switch.
If you have a bad ground on the tail lights and the common dual filiment lamps like a 1156 or the wedge based equivlent.. When you turn on the tail lights, power feeds back to the brake lamp circuit. When you use a turn signal power feeds back via the tail light elements to the brake light circuit via the other side.
And that kills the cruise.
I had a problem with the FRONT turn signal not grounding properly and it caused the same issue.
And when I got a new towed,, The ground connection on the socket for the towed (Motor home end) needed an upgrade as well.
Thankfully, though these things do tend to save me the cost of a hair cut.. Figuring them out IS within my skill set.