The V6 trucks all have a 4WD system, none had AWD except the V8 models.
What you have is auto 4WD, just like the newest 6th gen which are too, auto 4WD. That means in the auto position, it is in 2WD, RWD, constantly, until it senses a difference in speeds of the two drive shafts. Then it instantly(as fast as it can) engages the front driveshaft, by way of an internal clutch inside the transfer case.
So you should leave it it A4WD all the time, it does nothing until it senses a need for the front tires to be driven. If you mash the gas with any tire on a sketchy surface(ice, snow, wet leaves, dirt, grass etc), you should feel a slippage of at least one rear tire, and the engagement of the fronts. Often people have called it clunky, which is the feeling of when the front driveshaft is initially grabbed each time.
The V8 AWD has no delay and should never have any odd feeling when you hit the gas. On a wet road or partially in grass, the real AWD and the 302 will slightly spin a tire. I hardly ever feel that, but I remember feeling it constantly with my 99 V6 A4WD Explorer, I always had the right tires on grass or dirt along the edge of the road.