The 4S cannot be jailbroken on iOS 6.1.3. Only the 3GS, 4 and iPod Touch 4th gen can be tethered jailbroken on iOS 6.1.3. You can't downgrade your iOS with or without blobs on the 4S either.
I'm afraid that you'll have to wait for the next jailbreak release in order to jailbreak your iPhone. Evasi0n has already announced that they won't be releasing a jailbreak for iOS 6.1.3, so you may have to wait for a later iOS release.
Wrong. You can't downgrade the 4S at all, regardless of whether or not you have SHSH blobs. The only way to downgrade the A5 device is by having both iOS 4 and iOS 5 blobs. Since iOS 4 never existed for the 4S, it's impossible to downgrade any iOS.
There's no turning back bro, you can't take a back route to iOS 6.1.2, you fell right through the thin air. You cannot jailbreak the iPhone 4S on 6.1.3 as one of the exploits used by the evasi0n jailbreak is patched. You have to stay on that iOS until further notice and a jailbreak is released for 6.1.3.