The flashing lights you are describing are most likely the strobe lights. There should be one on each wing and another set on the tail. This is in addition to the position lights (Green and Red) and beacon (red flashing - like a police car)
It may be that the aircraft you were looking at simply had one of the strobe lights burnt out, and that's why you only saw one.
Alternatively, there are certain aircraft designs which allow for the selection of specific strobe lights on and off (although this is more for military aircraft who will be flying in formation than for civilian aircraft). If this is the case, then it's simply a switch in the cockpit - one of the Dash-8's that I currently fly has this modification, and it is really easy to forget that instead of one switch, it's actually four that you need to check.
Lastly, these strobes, by regulation, need only be seen through a specific arc around the wing tip, so it may also be that you were just at an angle that did not allow you to see the other strobe.
In any case, the strobes are meant for visibility in the air, and it's accepted as best practice not to turn them on until you're on the runway - they're quite bright to look at during a taxi! In saying that, every operator has different criteria of when to turn them on and off, so I'm sure someone else will point that out!
I hope that helps!
Note: edit for grammar.