Are you telling the brain to learn the tach signal after tapping in? You have to tell the brain to remember the tach signal presented to it. I install Directed and Compustar products, so I'm unsure how Bulldog does it. But a little Google-fu says it's a lot like Compustar. Start the car with the key, press and hold the foot brake, press and hold button 2 on the keyfob until the parking lights flash. And just so we're clear, you also have to change the tach menu setting to hardwire tach versus the default, which is probably a tachless setting of some kind.
I show black/green wire at any ignition coil. But any fuel injector is usually a better spot. I don't have wiring info for them, but pick an injector and tap into one of the two wires. Try to learn the tach signal. If it refuses to learn, tap into the other of the two wires and try to learn again. Should be zero reason this doesn't work.