I’m not sure I follow. The center diff is a manual cable actuated shift over to High or Low/locked unlocked. I don’t think cycling the engine will change anything.
Are you saying you shifted over using the transfer case lever (ball shifter) and when you shifted by back to, presumably unlocked/High, it didn’t work?
If it shifted back, the blinking Telltail light you’re probably seeing will eventually disappear, but the important part is that it engaged. If the shifter is in the high/unlocked position (top left corner), you should be go to go. If you got a bunch of grinding sound then you’re not and should try again
It also might be worth mentioning that the transfer case works in a box pattern. According to the brief I got at delivery, you shouldn’t shift diagonally, ie from unlocked/high to locked/low or unlocked low/locked high.
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