Evasi0n 1.4 has just been released to jailbreak iOS 6.1.2 untethered on iPhone 5, 4S, 4, 3GS, iPod touches, and all other devices. You can download the latest version of Evasi0n from here, and jailbreak using the instructions illustrated below.
The release of iOS 6.1.2 may have fixed the Exchange calendar bug that was eating batteries like tapeworm, but it looks as though it still hasn't prevented the Evasi0n tool from offering an untethered jailbreak. Seasoned jailbreak guru and Evad3rs member Planetbeing has tweeted the good news that his iPhone 5 is jailbreakable on iOS 6.1.2, and although he has yet to test other devices, it's unlikely they'll throw up any nasty surprises. This means that, pending a little more investigation of course, you can update to iOS 6.1.2 and re-jailbreak to enjoy the perks of an untethered jailbreak on your iPhone, iPad and iPod touch.