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What year is your truck? If it's an '04 you have CDL. If it's earlier a prior owner may have added. Also, is the transfer case shifter in a right-rear position or is it more center-right when in High range? Maybe post a picture of the shifter itself?
The '04 shifter puts the handle in the right-rear position when in High/Unlocked. A simple High/Low shifter is always centered left to right.
If you have an '04 and you can't get the shifter to move to the left to engage the CDL it's likely that it hasn't been used in a while an may need to be cleaned and lubed to function as it should. The '04 shifter in my '99 moves pretty easily right to left and back.
This may not help but when I bought my 04 the CDL had not been engaged in while and it was a bitch to move that lever.
The recommended method to is to be barely moving - you can walk faster - pop into neutral and firmly move lever all the way up to get into low. In my case very firmly. Then back into drive. Once you get into a new position drive a bit, it does not have to be far maybe 500 meters or so.
I did this 3 or times and everything moved much better, I make a habit of going through all the positions once every 10 days to keep everything happy. That might be overkill but I have no issues shifting anymore
The recommended method to is to be barely moving - you can walk faster - pop into neutral and firmly move lever all the way up to get into low. In my case very firmly. Then back into drive.
I don't think going back forth between Hi and Lo will do anything for the CDL part, only for the range selection.
With my '04 D2 I've always found (few times checked) moving lever to CDL from high or low is easy with no effort. Checke a couple of days ago and all good in high and low
If yours is a '04 with intact CDL you may need to look the linkage. If a earlier D2 it may have a CDL mod and your results may vary.
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I think I have an 03 one, although I am not sure. I have no problem shifting from high to low but it does not look like it can move to the left from any position.