Didn't get a drivers manual handbook with my Duramax.

On the gear selection - P,R,N,D.....and so on. On the far right there's what looks to be a small case 'L'.

I assume this is for the locking differential?

If it is - you must have to manually tap the gears up or down on the shift lever??

Thanks in advance,

Thinking that's Low gear. You should have an "M" which is the manual gear selector.

I am assuming yours is a 2005 or older. It is for Low gear. The G80 locking rear differential is automatic and really only works after you get stuck. What year is the truck? The 2006s were the first ones with the tap shift selector. Fill out your signature.

Sorry bout that it's a 2008 truck.

In service date of Dec 1st 2008.

Took a closer look at the indicator it's:

P,R,N,D,M, , ,l

Looks to me like it's either "L" or "l" or "1" for locking diff ?????

I tried it, still need to tap shift to move up a gear.

The M is for manual. Use the tap button to shift up or down manually as needed. If you want the 1st gear or low, and are going slow enough, you can shift the lever to 1 and it will go to first gear and hold it there, skipping all the other gears.

When "1" is selected, the truck will select the lowest gear possible given curent road speed.

Here's info from Allison:
http://www.allisontransmission.com/service/faq/index.jsp?CategoryID=11
http://www.allisontransmission.com/servlet/DownloadFile?Dir=publications/pubs&FileToGet=SA5521EN.pdf