Does the horn/beep sound somewhat similar to this one,
https://www.youtube.com/watch?v=1C7MDYSEH5g
Is the boat new to you?
While not listed below, sometimes low voltage has been known to sound the warning horn too but sort of with a broken/disrupted sound but with your system it should be more tied in due to the key is on but the engine is not running due to no engine oil pressure yet..... Also with the stern drive gear lube reservoir low it will sound the waning horn with the key on engine on or off.
MERCRUISER HORN WARNING SYSTEMS:
1995 – Current:
Models: 5.7L 7.4L 8.2L:
Inboard/Tow Sport/Stern Drive Carbureted Engines.
Horn Output: Solid horn on key on, but goes off when oil pressure switch sees 6 PSI on start up.
Possible Cause: Normal test horn.
Corrective Action: No Action Required.
Engine Usage Available For Consumer: No Action Required.
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Horn Output: Solid Horn (continues)
Possible Cause:-
-Oil pressure
-Engine temperature
-Low Gear Lube Reservoir
-Transmission temperature
Corrective Action: If possible, stop engine and key off to check possible cause for engine overheat and fluid levels in both engine and drive.
Engine Usage Available For Consumer: Proceed with caution. See dealer if no issues found.
Your waning horn may look similar to this design,
http://thumbs.ebaystatic.com/d/l800/pict/272094933577_1.jpg
Or maybe this design,
http://s399.photobucket.com/user/maniomp/media/boat/buzzer.jpg.html