I have a 67 which has the ignition on the dash. I think the 68 is on the column? ANy rate, I had a similar problem after I replaced the steering wheel. So assuming your horn works after testing by connecting to your battery, I installed an auxiliary horn button on the bottom of my dash.
I also noticed the connectors on the horn in the grill seem to fit loose. MMay want to check them for tight fit or corrosion. Did you check your fuse? I’ve also experienced issues with a good fuse, but very slight rust forms on the terminals. Just clean by lightly sanding with Emory cloth then apply some dialetrect grease to protect from future corrosion.
Good luck