Since you are new to Chinese Tractors here is what I have found working with 2 of them I have used. The 4x4 is easily engage while rolling and even making a slight turn seems to help. Trying to engage and dis-engage was tough when not moving.
The same is true for the diff locks on both.
Chris
Not sure about the Foton, but on my Jinma, the 4X4 and Differential lock mechanisms are two flat faced "pawl" devices that slide together and interlock. The pawl lookes basically like a 6 piece pie with every other piece missing. If you put two of these together, the 3 triangular pieces/teeth on one pawl will fit into the space between the 3 teeth on the other pawl. Because they are flat faced, they must be perfectly aligned before they will slide together. Like Chris said, rolling helps engage them, in fact, it is almost always a necessity, unless the teeth just happen to be in alignment when you pull on the 4X4 lever. To engage 4X4 or the difflock, while rolling(or with a rear wheel spinning
), I apply gentle pressure to the control lever, and eventually the teeth align, and it falls right into 4X4 or difflock. Comming out of 4X4 is easy, just put some pressure on the lever, and it may come out easlly, depending if the pawl drive is under load at that moment. If it is stiff disengaging going forward, try it while rolling backward... For the difflock, I almost always have to turn the tractor from right to left to unload the difflock pawls so the spring will dissconnect them...
If the foton uses the same mechanism for 4X4 or difflock, I doubt it is making your noise, as it takes a little bit of travel and some applied force to engage/disengage, and I doubt that input happening by itself.
Can you determine if it happens in 2 or 4 wheel drive? that might help eliminate the transfer case or driveshaft... If yours is like most of these chinese tractors, it is probably dead easy to pull the top covers and expose most of the forward gearbox for a visual examination. The rear differential and PTO gearbox is probably another story
A mechanics retrival magnet on a flexible handle is good for pushing down around the sides of the gears looking for any metal lying loose in the sump below the gears. You could have a broken piece of shift fork dancing around in there, occasionally falling against a spinning gear and being whacked out of the way by a gear tooth for it's trouble. Roll the gears over slowly by hand(will need to jack up a rear wheel, and or push in the clutch for this) looking for chipped gear teeth.
Better to find this sooner than later. As Greg mentioned, a stray piece of metal finding it's way into the wrong place will destroy a gearbox is short order...