An Australian Perspective
Flyer696,
What you describe as a recognition light (flashing on the wingtip) I would describe as a strobe light. In my flying career, these have been turned on entering the runway for takeoff and then turned off exiting the runway after landing. Sometimes in cloud, the flashing can be disconcerting, so they might be turned off for a period in flight in cloud.
What I know as recognition lights, are lights that illuminate the tail fin, and usually the airline logo painted on it. A mix of advertising the operator of the aircraft, and increasing the visual presence of the aircraft. In my curent operation, we use these recognition lights only at night, and only below 10,000'.