What is the implication if one of the navigation lights failed to function, would it affect the airworthiness certificate of the aircraft?
In the US, you would not be able to fly that particular aircraft at night and/or IFR since IFR flight requires all day and night equipment to be operable according to Title 14 Part 91.205. Only VFR day flight is allowed.
You would need to check your Minimum Equipment List and/or Kinds of Operation Equipment List to see if the manufacturer would allow flight with that particular piece of equipment inoperable. Then, placard the position light switch as inoperable. It would be best to get it fixed ASAP, just in case you or the next pilot to fly that plane has a flight run late.
If you are already in flight when you noticed that the position light failed, you handle it just like any other failure. Land as soon as practicable. To do this in the case of no position light while VFR at night, I would immediately get on flight-following and explain to them the situation. If you are already IFR, simply inform ATC of a position report with a safety of flight change.
I would prefer to land at an airport with an operating control tower with radar. I am lucky in the fact that I have a few nearby. Just be wary that the failed light is just a failure of the light. And, that it is not indicative of greater electrical failures.
Also, make sure your Transponder is operating in either mode C or S. And, make sure both your ADS-b in and out are currently operating as a safety net.