I am starting to understand this 4wd system now.
Tips for testing the actuator pump:
1. If it runs/pumps when the 4wd lever is shifted (key in ignition) and runs for ten seconds and then stops, there is a leak in the system.
2. If it runs/pumps for a second or two, it is functioning properly.
The 4wd light is activated when the pressure sensor in the pump reaches the proper level. I tested that out by plugging the hose, shifting it into 4wd, hearing the pump turn on for a second, hearing the pump shut off by iteself, and watching the 4wd indicator light turn on (for the first time since I've owned the vehicle). Therefore, it seems to indicated that a flickering 4wd light tells you the pump is turning off and on to keep the system at the proper pressure.
Conclusions to my troubleshooting:
My pump is working just fine and there is an air leak in my front diff.
Now I have an excuse to get manual hubs and permanently engage the actuator.