"Sput"
Here is another "fact". Polarity when connect directly to a 12v battery makes a difference as well...same symptom. That is what actually clued me into swapping the polarity to begin with. All wiring in the entire truck is new and I took care to ensure excellent contact points throughout. The horn has a dedicated ground.
The condition of the horn is definitely plausible and a likely contributor. Probably a little more fine tuning of the horn will make it work better. But now, it works flawlessly the way it is.