In addition to cruise control turning off and not working when headlights are turned on, the right hi beam headlight does not work. The bulb looked okay and the fuse was okay. Where do I start?
This sounds like a poor earth or ground.
Find the reason the right high beam is not working and correct that.
The cruise could be getting a weird input due to a poor earth, and safety causes it to default to off.
On my car the cruise control will not engage if one of the brake lights is not working... And will not engage if the brake light bulbs are replaced with LED...