Yes it does. The horn and the brake lights are on the same circuit and share the same fuse (#2 10A). The likelihood is that this fuse has blown.

The big question is why? Sometimes fuses just "blow" through poor manufacture, fatigue and bad contacts/corrosion. It could however be a fault with the horn, either of the stop light switches, the rear light cluster or in the wiring.

Try replacing the fuse. Turn the ignition on, but only try operating one thing at a time. This will help you isolate the fault (if there is one). First try the front brake, see if the brake light works and, more importantly stays working. Repeat with the rear brake alone and then, finally try the horn. If the fuse does blow at any point you'll have a pretty good idea which component is the culprit. If everything stays working, then you're good to go.

If the fuse does blow during one of the tests, then you'll need to isolate exactly where the fault (short to earth) is in what ever component/wiring that's is causing the blown fuse.

It could of course blow straight away as soon as you turn the ignition on, in which case the short will be in the supply wire to one of either of the brake switches or the horn switch

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