The L4 position switch is how the ECU knows if it is in "low" range or not. If that switch is not working, it won't engage the center diff lock when the shifter is in low range because it thinks it is still in "high". The other position switch on the transfer case tells the ECU when the diff...
I would check the L4 position switch on the t-case. It is similar to the position switch for the center diff lock.
https://forum.ih8mud.com/threads/cdl-transfer-case-position-switch-part-number.531497/