On 2003 Camry the high beam lights intermittently come on while driving. It only happens during cold weather. It happens mostly when turn signal is being used, specifically after the turn is complete and when trim signal goes off.
Since the problem is affeceted by the turn signals, the most likely caue would be the light switch. It might have to be replaced as internal contacts are most probably faulty.
It could also be due to the Body ECU and you need to have the system checked/tested to confirm the source.