First, If you have a factory horn relay, remove the cover and inspect the contacts.
Otherwise, You may have a weak connection (either in the steering wheel area or elsewhere) that only allows enough current for one horn to work. Put a voltmeter on each horn as you blow the horns and see if you're simply not getting enough voltage (and ultimately current) to blow two horns at the same time. Try installing only the voltmeter in place of both horns to see what voltage the horns are seeing under no load. Then plug in one horn and measure at that horn, and at the other unplugged horn. Then plug in both and test at each horn. Test all reasonable combinations.
If you don't have a horn relay, consider adding one, using the power to operate the relay from the one horn. Run a wire to the battery, use a 30 amp relay, and you can power 4 horns from a Buick Park Avenue, if you like.