first off,on that motor there is no alarm if the oil injection pump quits.
there is or should be a sensor in the oil tank that will if working cause an alarm to sound when the reservoir is getting low on oil.
when you turn the key on there should be a single long beep of about two seconds,that is to let you know the system is ready when you turn the key to the on position and it will go away once the engine is started.
on most boats,the alarm horn is located under the dash and you would not believe how many times I have found that little alarm plugged tight with mud daubers nests.
it may be that yours is bad,or has been unhooked because someone got tired of the low oil alert going off or the overheat sensor doing the same thing and just unhooked them instead of replacing the bad part.
those older motors also had an alarm driver module that depending on what sensor was telling it what would sound a series of different alarm sounds.
over temp was long unending beep,low oil was a series of beeps until the oil got critically low then it would become a long beep.
the alarm driver module was noted for going bad,they would do one of two things,either not sound an alarm at all,or,the alarm would sound non stop.
as Grouse said,dont unhook the oil injection system !! if you do and dont remove the pump and install a block off plate,the pump unless allowed to recirculate oil to the reservoir would run dry and seize up shearing the teeth off of its drive gear and those parts would end up in the lower crank bearing.
the biggest worry you have with that motor is make sure the crankshaft main bearing drain hoses are not cracked or broken off at their fitting,if allowed to run that way a cylinder will run lean and burn a piston.
you should see a hose coming down from under the flywheel to a tee fitting in the middle of the crankcase and a third at the lower end of the engine.
to see the center drain and bottom hose fitting and hose correctly,you need to loosen the ignition module assembly and swing it out of the way.
if the hoses look remotely weak,cracked,broken,replace them and to get the correct hose you will have to go to a dealer to get it as it is odd sized.
if that motor has had any care at all and ran with good oil and non oxy gas it will serve you well for many years.
while you are at it,check the fuel pump out,hopefully you wont find this but I would about bet you do.
the debris under the check valves in this mercury pump are from a failed fuel line.
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