When its in any 4X4 mode, its always on. Full time is a polite way of saying All-wheel-drive. The front and rear wheels move at almost the same speed (60% of the power to the back and 40% to the front if I remember correctly). This allows for enough slip in the system, that it doesn't bind up TOO BAD, but it will still bind a little bit in turns.
The Part time allows the front and rear wheels to spin equally (50 front and 50 back), and allows for NO slip in turns. This is when you commonly get "wheel hop" or "driveline binding'....in other words the pressure building up in your driveline is being released. Not good for it. Which is why part time must only be used in slippery conditions such as snow (NOT RAIN, this is what full time is for if needed) or if off road for added traction. Also, DO NOT use part-time OR 4-low on dry pavement. 4-low is for serious rock crawling or pulling a damn house down. Its quite possible that your system is stuck in either part-time or full-time. But to answer your question, no, it does not automatically switch back and forth b/w the two. You do the switching yourself by selecting which ever mode you need on the transfer case.