Whether you press EJECT while a game is running or at the start-up screen is irrelevant - the disc is still spinning either way. You will not damage your PS2 which ever way you swap discs...
I can't believe people are asking how to eject and swap discs on a PS2 - I mean, it's not exactly rocket science.
I've been ejecting discs both ways for well over a year now and have had zero problems with my PS2.
- S
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