OK, more questions..
Is the Vehicle re~wired?(new plastic coated wire as opposed to Cotton clad wire?) If not, on a 39 I am not sure about a stock relay, but I lean toward "I doubt it has one"...If aftermarket wiring it probably has..
And the second and more important question...I assume you are using an "Button" for a horn , not the standard GM horn setup..cuz...It's ground!
When you push the button on a standard GM horn button, it has a "Brush~like" device in the steering wheel that takes the black wire in the column harness , and GROUNDS it...this applies ground to the relay coil..which has power at all times.
If you are using it..and it is working for some reason, with 12 volts on it...you are very lucky! for some reason the column is not grounded and it's only a matter of time until it is..so the next time you push the horn .. it all goes up in smoke..(12 volts to ground..)
If however, you are using an aftermarket "Black Button or switch" I can see how that can work fine..however the safe way is to use the ground in either case..Assume every-time you hear a stuck horn, It's a ground hitting something on the horn button wires..Now change that to 12 volts..you have a burned up harness or fire..
To check if you have a relay now..in a quiet location, disconnect the horn at the front, and push the horn button..listen for a "Click" and track that noise down, you'll find the relay..If however you don't hear a "Click" you may not have one or it is inoperative..