The tach needs a pulse hot and a ground to operate. Depending how the boat was wired it could create a problem but I would expect it to be in reverse. Nothing working while disconnected

I have no idea where the book to my motor is. Was gonna trace the path and color of the horn wire to see what we might have overlooked.
Does the horn come on with the key switched on or only when the engine is running?

These pictures should be of the same set-up as yours as I have a 90 powerhead and early style harness. If you disconnect these 3 sensors and it still goes off you probably have a harness problem. There is also a chance that the self test portion of your hot horn has failed and stuck on. You can get a test light and connect the ground clamp to a 12V+ source and probe the brown hot horn wire and see if the light lights up. If it does then you probably have a harness problem. Also try unhooking the brown wire from your horn while leaving the key on and black ground connected. If the horn sounds it's defective, if not then your getting a ground in the harness. It doesn't take much to set the self test style horns off.

Here is the starboard overheat sensor.
http://i162.photobucket.com/albums/t...AFT/200E-1.jpg

Here is the port overheat, the one that hooks to the brown wire is the overheat and the white and black goes to the power pack.
http://i162.photobucket.com/albums/t...AFT/200E-2.jpg

And here is the fuel restriction sensor, you can also see the VRO amphenol in this one just to the right of the starter.
http://i162.photobucket.com/albums/t...AFT/200E-3.jpg

The first time the engine would run for maybe 5 seconds and then the alarm would come on. The second time it would come on after turning on the key.

Basically, the way the horn sitiation works is a constant hot thru the key switch, the ground will be derived thru the 2 temp sensors and any of the VRO system. If any of them trip it sends the ground path from the motor block to the horn.
You may disconnect the VRO and not interupt the water temp portion and visa versa.

Ferm, on the fuel restriction sensor, I should just disconnect the black wires?

One of them will hook to a ground wire, and the other should have a bullet connector on it. Unhooking either of them will take it out of the loop. Which style horn do you have now, 2 or 3 wire?

Both the black wires are grounded to the fuel pump mount. I pumped my primer bulb and felt some resistance and then the resistance gave way. I fired her up and got no alarm at all. I reconnected the temp sensors and still no alarm. This doesn't make sense though if the fuel restriction sensor isn't connected to anything. Starting to think some crud in the fuel line to cause the rough idling, but dumbfounded on the alarm.

I guess i need to pull the cover off the control box to find that out?

It sounds like the fuel sensor is connected and working and you did have a restriction and this would account for the rough running.