Lockers can click and chirp. Not sure if they can be adjusted.
Some can't, some can - it's a time consuming task, typically done by adding/removing shims behind the side gears or couplers. I have seen reports of spooled vehicles regularly driven on pavement "wringing" the drive shaft splines, but, who knows if that was caused by the use on or off road, because if it's locked and used off road, there's a pretty good chance is going to be driven hard.
To Scubaralf - you're asking us to guess what some previous owner installed in your rear axle - there are "spools", which are essentially a chunk of metal with no differential capabilities; there are welded differentials (sometimes known as Lincoln lockers - after the Lincoln welding plants) which are differentials that can no longer differentiate; there are selectable lockers, which the driver can lock and unlock and there are several different styles of non-selectable lockers, or auto lockers, which supposedly lock & unlock themselves as necessary - typically they are locked until they are forced to unlock by one wheel turning faster than the other as the vehicle goes around a turn.
This last type can be considered a full time locker as it is always engaged, or, as Phase change has suggested, a full time locker would be a Lincoln locker or a spool - my point is - there's no way we can do anything other than take a wild guess as to what's in your car.