Normally if it has locking hubs, it has the part-time kit.
If it does have locking hubs, here's how to tell if the part-time kit is installed. Put the hubs in free, put the transfer case in 2H. Now put the transmission in Drive. If it drives normally, it has the part-time kit installed. If the front drive shaft spins but you don't go anywhere, it is unmodified. If it is unmodified, turn the engine off before shifting out of Drive so you don't trash the pawl on Park.
The shift pattern for a modified NP203 is 4L-2L-N-2H-4H.
Some tips (some of this is WITH the part-time kit; should be obvious which):
You can't shift the NP203 through neutral unless the transmission is in PARK or the engine is off. Basically, if the transmission isn't in PARK or the engine off, when you shift the NP203 into neutral, the output shaft of the transmission will start spinning (even in Neutral), and you won't be able to shift out of Neutral into 2H or 2L because the shaft speeds aren't the same.
You can shift from 4H to 2H or from 4L to 2L at any time, whether on the move or not. You can shift from 2H to 4H or 2L to 4L while moving if the hubs are locked, but only when stopped when the hubs are free. Basically, in 2L or 2H, the front driveline parts are only spinning if the hubs are locked, so the speeds of the front driveline and the rear driveline are matched and you can make the shift. If the hubs are free, in 2L or 2H the front driveline is stopped, and you have to stop the vehicle to match them so you can shift.
Being a full-time transfer case, the NP203 has no oil pump to feed the rear output bearing. The chain drive to the front flings oil on the inside of the case, and a pair of oil ways on the inside of the case deliver oil to a small gravity-feed reservoir over the output bearing. Drive it around in 2H all the time with the hubs unlocked and you will run the reservoir dry and eat rear output shaft bearings, the replacement of which is annoying.
The solution to that is, when the hubs are unlocked, to shift into 4H for the first couple of miles every day, or when traveling long distances the first couple of miles after a gas fill-up or rest stop, to engage the chain and fill the reservoir. You can then shift to 2H while on the move. If the hubs are locked (I leave mine locked during the winter when there is snow on the ground), then you don't need to do this because the chain is being spun from the other end and is keeping the reservoir full.
Annoying shifter rattles can be because the handle that sticks up into the cab is not the actual shift actuator. The pretty chrome handle in the cab is bolted to the actual shift actuator under the boot. The bolts come loose, and then the thing rattles. You can tell because the shifter will have free motion without changing modes. Take the boot off and tighten them.
The transfer case shifts should be very smooth and easy. If they are not, your shifter is full of road grime and dirt. The solution is to remove the boot and hose the thing down with WD-40 or PB Blaster or Silikroil. Do that and let it sit overnight, then do it again the next day. Finally, run some oil down through the shifter to lube it. Do this all out over some gravel somewhere, or over a pan, because you will make a mess.
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