Differential locked
#1
#2
#6
the differential is probably not locked, since you're in an '02 and it's highly unlikely that you have a lockable central differential unless your truck has been retrofit. the transfer case is slipping into neutral between the high and low ranges. shift into low, then shift back into high and see if that cures the problem.
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DTwo (02-09-2019)
#10
That light is for the center diff lock. From the factory your truck did not have a mechanism to engage the lock. It could be a wiring issue to diff switch (I can lock my diff but the switch no longer works). Check to see if your diff is actually locked by driving in a circle on dry pavement with your steering at full lock. The tires will skid/scrub on the pavement.