Changing battery fixed 4x4 actuator?

I just changed the battery on my 4.0 2011 Ford Ranger XLT and my broken 4x4 actuator immediately started working. The 4x4 light had been stuck on but the 4x4 wasn’t activated. I just changed a dead battery and went to back out of my driveway and lo and behold, the 4x4 was on. Tested turning it on and off and it works perfectly.

Why would replacing a battery fix the 4x4 actuator?