If I had it to do over again, I'd have bought a spectacle or helmet mounted mirror, if only so I could turn my bicycle upside down and rest it on the handlebars and seat while working on the lower parts of the bike.

That said, the motor-scooter-style mirror I have mounted on my bicycle works fine for me. I hate those curved mirrors that make things look smaller/further than they appear.

I agree about not relying on sound, especially at my age, where hearing is no longer the most fine-tuned of my senses. I've often had cars get right up behind me before I can even hear them at all.