Sending "Blink" to pin 12 is causing on-board led to blink?
See Have I bricked my Arduino Uno? Problems with uploading to board

As I state on that page, if pin 13 is set to input the LED may turn on due to being driven by an op-amp. A nearby pin turning on may be enough to cause that effect. Try adding:

 pinMode(13, OUTPUT);
 digitalWrite (13, LOW);


See if that changes the behaviour.