4wd light blinks until I restart vehicle

My 2002 4Runner SR5 blinks the 4wd indicator when I engage with the button, and will not stop blinking until I shut engine off and turn back on. Disengaging it works right away, but engaging it is when it acts up. I can sit in it with the key on, and engine off, and engage 4wd. I feel and hear the actuator move as it engages, but indicator light on dash does not stop blinking until I turn key back off and then on again. I’ve tried rocking from Drive, to Reverse, and back and forth, but to no avail. Is there a sensor that is acting up? Is this how it acts when the actuator isn’t functioning? I tried to find a similar post, but nothing quite matched the symptom I have.