As far as I can see from looking at realoem.com, the transfer case is the same in the manual and the auto. It does seem that there was a period in 2006 & 2007 that there was a different part number though.
RealOEM.com - Part Search
https://www.eeuroparts.com/Parts/677...0-27103455137/
Critical as you are probably already aware that the front and rear tyres need to have the same rolling circumference, any discrepancy there will result in the transfer case working overtime.
I have read over the years that a loose or incorrectly sealed gas cap can trigger a check engine light, though I have never experienced it personally.
Good luck getting it sorted.