Loose fuel line clamp allowing air to enter? Poor seal on the water separator bowl? Notice any air bubbles in your low pressure fuel filter? You don’t mention smelling fuel so I would concentrate on the suction side of the fuel line, downstream of your low pressure fuel pump.
Sounds like your engine is going into fail safe mode. Below is a chart of the error codes, on the right column where there is a yes then the ECM will limit the revs to 3000rpm. When you turn the key to on(not start) do you get the self diagnostics buzzer and I believe all lights light up for 2...
Get a genuine Evinrude service manual, often generic service manuals will be missing info and or wrong information. As Racerone stated get a new water pump, not just a new impeller, the entire water pump. When running in a barrel ensure the entire water pump is submerged plus 2”-3”.
I’m no electrician but it looks like if you ground the green and give the blue 12 volts it should buzz. Could be a bad connection, corrosion somewhere. Put a volt meter on the blue, turn the key to on(not start) and see what you get for voltage. At this stage you don’t know if the buzzer is...
You have fuel to the carburetor intake (end of hose) after it stalls or won’t start, is there fuel in the carburetor bowl? Are the spark plugs wet? Trying to determine how far the fuel is getting or not. I think Suzuki has a warning light to flash codes for malfunctioning engine, not sure with...
https://peparts.honda.com/marine/portable-outboard-engines/bf/BF5/BF5AM-SA/illustrations
Try this website. Your missing a few letters behind BF5 but should be a good place to start
From a 2009 DF90A. When you expand the the screenshot to read the wiring schematic if it’s too blurry send me your email and I’ll send you a higher definition screenshot. It’s not your engine but I’d bet Suzuki has standardized their wiring.
The tach needle will jump to the appropriate rpm number. Sounds like the tach is working fine. The buzzer will alert you to fault codes if thrown so it would be nice to get it working. Sorry can’t help you there