Sounds like it. Horn is causing the spike that puts the fuse above its threshold. Easiest thing to check, is it the right fuse? IE: maybe its a 10 in there instead of a 15 like it should be? I am sure one of the electrical gurus can chime in but often times it is possible to use a larger fuse without harm to the system and it may be just enough to correct your issue.
Are the blinkers and horn stock? If you are using an after market horn I would recommend a relay with an inline fuse directly to the battery (makes it louder in most cases too), this could also cause your problem since aftermarket horns need more than the factory meeper.
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