From your description, it looks like the hubs are engaging and disengaging properly. Other than finding a cap, I don’t think you have anything to worry about. Post a thread in the parts Wanted section to see if anyone has an extra or oneleft over from a switch to manual hubs.

Regarding your question about axle rotation, thanks to the front differential, any rotation of the driveline will result in axle rotation. Basically, you can’t have one turn without the other turning. So from the light’s perspective, driveline and axle rotation are one and the same.

I hope this was of help. Enjoy the snow (in 4wd).