You have a simple magnet and coil generating the AC pulses in the sensor. It would be normal for the voltage to rise when speed increases.
The other end of the wires must complete the circuit in order for it to work so YES, you can check continutiy at the tach end of the wires provided you have access to them.
With voltages these low, wiring problems occur with the slightest leak of either water or oil into connectors or wires themselves. Even when all connections are clean and sealed, signals can get lost when they start out at .52 volts. One tool to use in this event would be Radio Shack's Contact cleaner, it will clean connections and prevent further contamination if used with current weather proof connections likely to be found in your tach sender circuit.