Hi there, is the engine a 2 or 4 stroke? Is the engine serial number handy?
Do you happen to have/still own the owners/operational manual from new? If so there may be other listed warning horn message that might not be found inside a service manual...< That's according to a service manual like found on page 178 linked below.
Does your engine/boat have a smart-craft type gauge of any kind? If yes or no it may help show if there are any active faults via an icon message in the corner or digital display....If you don't have a smart-craft gauge you may want to consider getting one as the costs of some of these have come down over the years and it may help give an indication of something.
Do you know if the dealer connected the engine up to any DDT type scan tool which may have looked something like what's in the following service manual link and when over everything with you,
http://boatinfo.no/lib/mercury/manuals/150efi-175efi-200efi.html#/88
^ Did they mention if any of the fault light indicators were on as noted in the first link/page above of the DDT ?
If you have a smart craft type gauge, then one thought would be to check to see if the water depth finder gauge is turned on or off as I do believe that function of the system also sounds a warning horn at first key up....Maybe it got turned on all of a sudden/somehow/by someone and not really remember, etc...Again just a thought to check if you have a depth gauge of any kind and inside the smart craft gauges as it could be sounding two horns at key up.
Most of the listed warning horn beeps for the 2 strokes are either 4 beeps or continual but that mentioned you'd be surprised at how many boat owners over the years would chime in on these forums saying I'm getting a different number of beeps then what is listed in the manuals.
The following pages are of some guides to look over, you'll have to click on a few next page arrows to turn the pages for a bit more info as maybe something will standout to you,
http://boatinfo.no/lib/mercury/manuals/150efi-175efi-200efi.html#/170
http://boatinfo.no/lib/mercury/manuals/150efi-175efi-200efi.html#/178
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http://boatinfo.no/lib/mercury/manuals/150efi-175efi-200efi.html#/180
http://boatinfo.no/lib/mercury/manuals/150efi-175efi-200efi.html#/194