Possible solution...on my 91, first there is first the vacuum operated
unit under the battery, then lines that go to a vacuum switch located in
the transfer case activated by a lever....the switch went south.
I'm not familiar with your push button system...sounds like there is a
solenoid actuator under the dash
Check that the vacuum lines are all attached and working.
Maybe use a hand vac pump to actuate the under the battery diaphragm
unit and see if the light goes out