After speculation that iOS 8.1.2 was still vulnerable to the TaiG jailbreak, the TaiG team quickly released an updated version that supports the latest iOS version released today.
TaiG notes that the new version of the utility, 1.2.0, supports all devices running iOS 8.0 to iOS 8.1.2.
You can download the TaiG utility for iOS 8.1.2 from here. Since iOS 8.1.2 provides no major changes other than bug fixes, it is not a necessary update.
Be sure to check out the BAW Jailbreak Wizard for instructions on how to jailbreak iOS 8.x!