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How old is your car battery? As batteries begin to die in today's vehicles that are essentially rolling computers, they can sometimes cause very strange things to happen. When the factory battery in my wife's 2006 Jaguar XK8 began to die years ago, it would randomly pop the trunk open. A new battery solved that issue. As I said, very strange indeed....
It is indeed strange but there are few things that can be the cause of strangeness.
Is there lint in and around the remote button? This maybe accompanied by faster that normal drain of Key Fob battery? You may like to observe the red lead in dark environment and confirm it is not lit.
Are there other Lexus/Toyota smart key enabled vehicles near bye?
Do you carry more than one smart key?