I'm no help at all but, for what it's worth I had the exact same issue with my 5 on 6.1. None of my recalibration attempts rectified the problem and its actually quite difficult to see the screen in sunlight after it dims which is a problem since I work outside. I restored as new to 6.1.2 which immediately fixed the issue and have not JBen since.
I'm watching this with interest hoping someone has some help. I would love to JB again before 6.1.3 is released but, this is the one niggling problem that put me over the top.
My jailbreak was with evasi0n 1.2 and my only tweaks were 5 Icon Dock, NC Settings, Activator, BiteSMS and iCleaner. OP, do we have any in common here?
I had jailbroken again with evasi0n1.5 just to fix the bootup time & brightness issue, but NO diff.
The moment i had only Cydia(plus default tweaks) the Home Screen dim was 45secs &
Lock Screen dim went up to 25 seconds(i'm OK with that) from 5secs.
So i don't know what's going on here

as some folks say this is an iOS 6 bug while some suggest it's Mobile Substrate.
Tweaks i normally use - SBSettings(with few addon toggles),
Missionboard,SwipeSelection,iCleaner,AppInfo,Privacy,Winterboard,BiteSMS.