Bench Testing '64 Impala SS horns

If I understand what you are saying? both horns do essentially the same thing? And that is they do not properly sound, but make more of a stacatto sound.

Might be your jumper wire is not large enough

Might be the bike battery does not have enough suds

Might be you are not holding them tight enough, and the vibration the horn makes is causing a sort of self oscillation.

I recommend you do something like clamp (vise grip) a ground wire to them, or use one or both jumper cables, and use a larger automotive battery.