The generic Marinette schematic was furnished to me by another member -- I simply drew it up and stuck it on the web, so I cannot vouch for the circuit. My boat had no wires...
Generally, alarm systems use either series or parallel circuits, and the sensors are either normally closed, or normally open, respectively. "Normally" means the "no alarm" condition.
Series circuits have the huge advantage that they sound the alarm if any wire connection is broken. That is what the schematic shows, perhaps others will weigh in to correct it based on their own boats.
Parallel circuits, like the one I use, can use alarm switches that are connected to ground. I went that route because the engines came with normally open "one terminal" switches. Nothing in mine is stock Marinette.
You are quite correct, the alarm horn needs to be a three-terminal device. I drew it to the old Marinette schematic, but there must be a ground on it somewhere. Sometimes these things are informal -- grounded thru the panel or whatever.
Please, all, send me your schematics along with the year of your boat, and I will post same and try to make some sense of it. Eventually, it would be great if a first owner could just look up the year of his boat and then download his schematics.... It would have saved me a lot of work if I had had something like this when I first started Marinetting.
1975 32' Flybridge Sedan, twin Perkins 6-354 diesels, 1:1.53 velvetdrives, 16 X 19 props. Merritt Island, Florida