TL;DR
Agreed its the TCase actuator. This is the thread I would follow. I haven't done it yet, but have all the parts and this is where I would start.
Fixing the transfer case shift motor leak from within..
Long story:
I manged to induce the leak (i'm assuming) when I test drove the car. I bought it from a private seller, a nice couple in their early 30s who I would assume used it for their weekend hiking and biking adventures, so I wasn't too concerned about getting scammed. It was an 04 v8 w/ 178k when I bought it. First inspection looked good. No visible leak, and under carriage didn't show any signs of a recent cleaning so I was confident there wasn't a leak. It had recent MD inspection (very through) and fluids looked good. On the test drive I made sure to exercise all the 4wd modes to ensure the actuator worked after reading some of the use or lose threads on here. Worked like a champ bought the truck, no issues. A month later I notice a tiny drop on the driveway and after some research I figured out where it came from. Could be coincidence, but I'm assuming I probably introduced a tear or something in the o-ring when I used it. I contacted the previous owner and inquired about it, and she insisted that she never used the center diff lock, and was frankly afraid of the button.
The point of this long story is that this was 4 years ago. I'm not sure how bad your leak is, but I haven't fixed mine. It does leak a bit. I tried the Blue Devil stuff once, but probably less than I should of for fear of ruining the other gaskets. It did appear to work for a while, but leak has since returned and I haven't' tried more. Stop-leak seams to be a hit or miss fix. I just keep a cheap gallon of gear oil on hand and periodically check and top off the TCase and before long trips, but it never takes more than 1-2 pumps before it starts oozing out the fill hole. I do think based on the size of the drops in the driveway that it is getting worse. I actually have all the gaskets, just haven't taken the time to try and replace them.