Brake lights do not turn off Cruise control does not work

If cruise control main light comes on but you cannot set a speed (no set), you could have a bad brake pedal switch.
(If the cruise control light comes on, chances are that it is NOT a fuse issue).
Some vehicles have two switches (one for brake lights and one for cruise control cancel) and others have a multifunctional, single switch.
The function to cancel cruise control is very sensitive so it only takes a small movement of the pedal to cancel cruise control.
You can try lifting on the brake pedal while trying to set the cruise, but this does not alway work. Replace switches are pretty cheap (less than $30) and pretty easy and quick to replace.

Well before you listen to all these people and do all kinds of crazy random replacements I'd suggest the very simple very easy solution of checking the fuse. If the fuse is bad it's a 3 dollar replacement. If that doesn't work I'd replace all the bulbs, more expensive but cheaper than the control switch. If that is bad it's also a fairly easy fix but a little more pricey.

I would check the turn signal switch. The cruise and turn signal are on the same switch. The brake lights go through the switch before going to the brake lights. And the turn signals don't work with the ignition off.

This problem is caused by a defective brake light switch or a switch that is not adjusted correctly, when the brake pedal is not being pressed the button in the center of the switch should be depressed, if it isn't screw the switch clockwise to adjust it., the switch is located under the dash at near the top of the arm the brake pedal is attached to, it is easy to replace and fairly cheap here is a price and picture of the brake light switch in your Honda. If you have cruise control the switch is slightly different, so i have included both pictures and part numbers.

AIRTEX / WELLS Part # 1S5431
With Cruise Control $16.33
AIRTEX / WELLS Part # 1S5681 Without Cruise Control
$14.37

the biggest thing with cruise control is to make sure all teh brake lights work. They shut the cruise down is inop

The break lite switch is located behind the break pedal and it probably doesn't replaced it is probably just stuck. Its fairly easy to get to .

If all the brake lights are out it is likely your stop lamp switch is bad, it controls lights and cruse, and also supplies input to ecm/tcm. The old ones would just pop apart, you can put them back together but to replace the switch it is only 20-30 bucks. Try that.

This works...the cruise is directly tied to the brake lights...when I replaced the brake and side light bulbs on my 2004 Santa Fe,,,the cruise started working with no other adjustments. It must complete a circuit or something.

check the fuse and relay, or you may have vacuum leak at the cruise diaphram.

I would check the easy things first. That is the brake switch and the clutch switch (manual trans). Drive down the road and pull the brake pedal up with your foot and then try to set the cruise (same with the clutch pedal). Also the cruise requires that the brake light bulbs be in working order (and that there are no LED brake lights). Check fuse numbers 53 54 and 59.
The high beam problem might be related to the cruise issue, but I can't think of a reason why.