In my (limited) experience, this 4X4 light will come on for numerous reasons. Mine was while dealing with the front brakes I had the ABS sensor blue plug undone while doing some test drives etc. The brake/4X4 was lit up. When putting it all back together the ABS was plugged back in and light was gone. So, an ABS fault will trigger it as well.

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Dave S.
Northeast
2003 4.6is
2005 E53 4.4
2003 E39 Msport(a REAL ONE!)
1959 Fiat 600