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Hang on, if you operate a 5A device for 1 minute then you'll use .083Ah, whereas if you operate it for 1 hour you'll draw 5Ah, correct? Therefor total current drawn will increase with the period of operation, if I'm right? I think we both meant more or less the same thing there, I just got my terminology wrong.
You're right, I think you are saying the same thing...what you are calling total current drawn is energy consumed, which is actually power * time. Remember, current is actually coulombs per second, that is I=Q/t, therefore Q=It...for example, if we have a 5A current flowing for 30 minutes, we have a total of 9000 coulombs of electron charge. This would just be a silly way to express energy consumption, so we use Ampere/hours instead...just makes more sense.
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Doesn't a simple press button counts as a capacitive device during initial contact due to contact bounce? Which would mean even in this simple DC device there'd be a higher peak current drawn when it's first started?
Nope...the horn winding is a coil of wire, which means it has inductance and resistance. And contact bounce is really only of any concern in digital communications circuits.
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However I still maintain that installing a relay in this case is so simple & cheap that there's no reason NOT to do it.
Like I said, in my opinion, if a person likes to tinker and play, installing a relay certainly isn't going to hurt anything (assuming it's installed properly!  ), but I personally wouldn't bother.
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