Since Batman doesn’t wear glasses and has a mask, I feel like it’s just as likely he’d have a like a smart glasses type thing built into his mask. So he really wouldn’t have to look anywhere but the notification would just be a translucent overlay.

Or maybe full coverage heat retardant smart contacts, so they protect his eyes from any debris/explosions. Kind of like what Tom Cruise wore to perform the outside the plane stunt in the last mission impossible movie. Covers the whole outside of the eyeball so the wind does dry out your eye or make it so you can’t see.