Why would both wingtip lights be red?
You might have been seeing a general aviation aircraft from an orientation similar to the one pictured.



You'd see the left navigation light which would be red.

The rotating beacon would also be red, but if the airplane was positioned like this and the beacon was the rotating, not blinking type, you might just see two mostly constant red lights. Being that it was dark you might mistake the second red light for the navigation light on the other wing.

It is becoming more common on general aviation aircraft to have a pulse option on the landing lights. I flew for a 135 operation for a while under which our contract required this to be installed and operational for all our aircraft.

This seems to be the simplest explanation for what you are describing. If we consider Occam'z Razor it is likely to be what you saw on the occasion you described.