Switch By Handbrake ?

Possible that you can take a picture of it and post it on the forum? Could be almost anything - especially if it was an aftermarket setup. Only factory option that I've seen close to the handbrake is for AWD Corollas only, center differential lock. But that is usually up higher on the central console and pretty clearly marked.

Also depends on what market the Corolla is - most members here are from the US, if this is from any other markets, like JDM/Australia/New Zealand/UK/Europe markets - might be an option we don't have here.