When I engage my 4x4 the light on the dash will turn on then turn off. Meanwhile the 4x4 is engaged and working. What could cause this? Any insight would be appreciated..

 

Welcome to the forum

The 4x4 system in Rangers changed a few times over the 28 years they were made, 1983 to 2011
So your Rangers YEAR would help

Best guess would be the Contact Wheel in the shift motor is dirty

You can see it here, not hard to check and clean, pictures 5 and 6

 

I have a 2004. I took a look at the transfer case and it's not dirty. Put it in 4 wheel and are moved no problem

 

The contacts inside the shift motor are not visible, and it would be corrosion on the contact surfaces

2004 has 3 parts for 4WD system
The dash switch, just 3 resistor inside, unless physically damaged these rarely fail
The 4x4CM, control module, behind the radio in 2004, these are failure prone, most common failure on 2001-2011 Ranger 4x4s
The shift motor, only moving part in the system so it will wear out over time, shift to 4low and then back to 2WD once a month, just sitting in driveway, this keeps brushes and rotor clean, and contacts

So try shifting to 4low(and see if 4low light stays on) and then back to 2WD, then to 4high to see if 4high light stays on after that, that might clean the contacts in the shift motor
Instruction for shifting to 4low on the back visor usually
Trans must be in Neutral(automatic) or clutch pedal down all the way, to shift to 4low