I have a 1996 Honda BF-50 and have heard the alarm on 3 occasions.
This may help. Check the drive really carefully. These engines have THREE intakes.
You see 2 with the decorative grilles on the vertical plane under the prop shaft. There is a third intake horizontally on the underside where the unit flares out.
I don't know how else to describe it.
Chris' posting below reminded me that one of the seasoned "experts" at our yacht club, walked me through how to winterize the engine about 5 years ago.
We fiddled and farted for a couple of hours with earmuffs and hoses, but kept overheating the engine.
When I replaced the impeller, the dealer showed me the secret of the third intake.
The problem when using earmuffs is that people in general don't know how to use them correctly with the Honda outboard. They have to be sealed properly and flowing a good amount of water. You're surely going to get squirted to get this to occur! Even then, it takes several seconds for the impeller to prime, which during this time it's running dry. When earmuffs are used improperly, the outboard could be running alot longer with a dry impeller. If there is no water coming out of the peehole, then you're asking for it. My garbage can approach ensures the impeller never runs dry.
-Chris
It's very possible that by tilting the engine, you exposed the horizontal intake and the cooling loop ran dry.
Ralph k.
PS
Although I think my engine may have lost a bit of it's original "snap" it still performs very reliably after 12 years.
Top speed loaded for cruising is 15 Statute MPH. There are no plans to replace it.