Intermittent backlash in drive train appears to be between transfer case to front diff in 4th gear on bitumen when centre diff lock engaged no more backlash. mainly occurs when at a constant speed ie 70 to 90 ks

that 4wheel drive is engaged
If the vehicle is an ALL WHEEL DRIVE vehicle there is a differential in the transfer case and although it is always in 4 wheel drive that differential allows the axles to turn at different speeds like when going over speed bumps
but it has a button to lock that diff up and by having that light on (providing there is no fault) the vehicle now has permanent drive to both axles---a condition not desirable when driving on hard surface as it causes torque wind up in the drive train which causes excessive wear in cv joints , splines, and in the teeth and gears/chain in the transfer case and gear box
take it to an accredited service shop that has experience on your make of vehicle and have the problem properly diagnosed as prolonged use in locked 4 wheel drive is an expensive exercise

it is all wheel drive so realistically the answer is ---no
However if you have a center diff lock switch to make it 4wd then --yes -- you can as that will lock up the diff in the transfer case
Will it damage the transfer case ---no--as there is no front drive shaft( you took it out) to cause a torque wind up problem in the drive train
AS to the park selection -- that is a physical connection of a pall in a ring gear in the transmission and the park action would be the same as in a 2wd vehicle
remember that is a requirement by law to engage the park brake and not to rely on the park selection of the transmission

the first place to check is then rear drive line "U" joints as fail on a regular basis and can be not allowing the shaft to turn properly
T check for diff , jack up one side and engage a gear
if the wheel spins then the diff is turning but if it makes a bad noise (all will rumble a t a low level in this position) the diff will be faulty
It is possible that a joint flange has come loose and the bolts are jamming on the back of the transfer case housing

Someone will have to go under and check the linkage is working when the 4 wheel drive is fully engaged and not just moved to a neutral position.

IT is a constant all wheel drive car which means that all 4 wheels are driven all of the time . There is a differential in the centre that allows for different speeds between front and back while driving such as going over bumps . When you engage the 4wd button you are in effect locking that centre diff so that both front and rear axles drive together. If you have it so that 4wd is not engaged (selected ) and there is no drive action to the rear wheels that then indicates that the shaft in that centre diff is not connected in the side gears ( stripped /broken) and it has been in 4wd all the time so that it could be sold

IF you are in constant 4wd then you will not have a centre diff unless you have an AWD. The difference is that AWD transfer cases have a centre diff that allows different road speeds between the front and rear diffs as in going over speed bumps and dips ion the road It is the same operation in the front and rear diffs that allow one wheel to go faster than the other when cornering. However in 4wd drive there is no diff action in the transfer case and both front and rear axles drive at the same speed regardless of speed bumps and dips in the road . This action produces what is known as torque wind up which results in the handling characteristics. This torque wind up places stress on all the drive line train and results in failures such as .that you describe.. This wind up is not noticeable when driving on loose surfaces slippery surfaces or in mud as it is allowed to escape when the wheels spin . If you have an AWD with diff lock capabilities then check that the diff lock is operating correctly

all wheel drive vehicles have to work at both ends all the time unless you have a major failure in the drive train. That is why it is called all wheel drive as opposed to 4 wheel drive. With 4 wheel drive you have the option of rear wheel drive or 4 wheel drive and normally in a high ratio or low ratio gear selection. With some all wheel drive vehicles there is a selector that locks the middle diff and creates a 4 wheel drive option without the high/low gear ratio option. So in practice if the both front wheels are in the bog then there is no all wheel drive as the centre diff is working as it should and placing all the action in the rear wheels which will not be turning as they have traction so the front wheels spin faster.. If you have a centre diff lock option ensure that it is operational.

Does it have manual locking front hubs? Some people fit these to full time four wheel drive vehicles to reduce driveline effort and increase fuel efficiency. The issue is that the drive from the transfer case will find the path of least resistance which if the front hubs are not locked power will be sent through the front diff and only spin the front drive shafts. To ensure drive power is sent to the rear diff the centre diff needs to be locked. If you do have manual locking front hubs try putting them in the locked position and leave the centre diff button off and try going for a drive.

Do you have the front hubs disengaged and the shift lever in 2wheel drive. If this is the case, the tyres will fight against each other while turning on bitumen.

The lights can come on wihtout the transfer case really working..the lights are actvated by a simple switch and only indicate the switch has been depressed.

It's sounds as if you have a problem with the lickage, or maybe damage inside the transfer case itslef