Don’t know the vehicle but I’m wondering if the problem is with the Central Door Locking System or perhaps the vehicle key fob.
Here are some composite images taken from the 2006-2012 Mitsubishi Eclipse & Spyder Service And Repair Manual Circuit diagrams and the 2nd Component Locations sections of the manual which show the two operate circuits for the horn, the location of where the two circuits are connected together and where the ECU is located.
(click on images to enlarge for better viewing)
Since you have proved that the steering wheel horn circuit is not the problem, the only other circuit for the horn is from the Central Door Locking System circuit which operates the same horn relay.
Not sure what you meant by “….continuously going off…”, whether this meant that the horn was on all the time or was sounding like a car alarm going on and off continuously, that’s why I mentioned the keyfob as it has a panic button which when pressed should activate the horn. At least I think that is what it does when reading the owner manual for the vehicle. Perhaps you could remove the battery from the keyfob and check. Just a thought.
If it is sounding continuously then you may have to check the circuit from or in the ETACS-ECU.
Hopefully a start.
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