Welcome to VMF. If you have both horns connected do the both blow if the engine is running?
On my 68 if the car has sat for several days or I've played the radio without the car running the battery is just slightly down, maybe just barely 12V. If I push the horn ring
only one horn blows. Start the engine...they both blow.
The two horns are in effect connected in parrallel so two take twice the current as one. These old fashioned vibrating horns when a few years (40?) old need a little more current to wake them up kinda like me! Meanwhile the 40 year old wiring, regulator etc. give a little less current. Remember it's current that makes things run.
My '64 1/2 vert. Ordered May '64. D code 4 speed, handling package, caspian blue, accent group, Ford blue manual top.
'68 vert. driver. Owned since '77. C code AT, AC, PS, P disc B, PT lime gold, standard black interior and top. NOS RF fender and left quarter.New top and folding glass.