On the back of the tach there will be the wire landing posts. I believe "power", "common", & "signal". If your DMM has the feature to measure hertz (Hz), then select this and measure between comm & signal with the motor at idle. If you see a measured value, you can further test this with a little fast idle to see the Hz increase with increased RPMs. If so, then this will tell you that your tach is toast if you don't see the needle move accordingly.
For the motor position, my Honda BF 50s have the tilt sensor located on the left hand side of the motor about mid-transom. This little black sensor has a lever arm against a fixed part of the motor that moves the lever when the motor is trimmed. When nosed down the lever arm is pushed. When nosed up, the lever arm has a spring return. I believe this sensor is nothing more than a little potentiometer. What happens is that this gets gummed or salted up and the spring return cannot overcome the stick.