Certainly the diode could be the problem. The anchor light gets power with both positions of the switch. The nav lights are excluded by the diode when in the "anchor light". There should not be a red and green navigation lights only circuit.
I would think if the diode failed, the white light would be on in both positions, and lack of the red and green???
Diagnosis involves getting a look at the switch from the back. Using a digital volt meter and measure voltage when the switch is in both positions. There should be 12V to white light in both positions, and power to the red and green only in the "Navigation" mode.
Some digital volt meters have diode testers also.
On the Fluke multimeter web site is a tutorial on testing diodes with a standard voltmeter.
Let us know what. you find--.