Rear end problems

OK so I just got my car running and took it out today. It has 3.73 gears and a detroit locker in the rear end. It will lock in sometimes and sometimes it wont. Anyways I was doing a few burnouts and launching it a few times and the left tire was spinning? I would think if im going straight the right tire would spin or both would not just the left side? Say I go around a corner I can hear it unlocking and feel it lock back in.
 
are you sure it's a locker...have you seen it or were you just told it is

Yeah I'm pretty sure its a locker. When I go around a corner it is clicking and when i start to straighten it out it clicks really loud and you can feel it. Also I can look in my rear view mirror and see 1 tire mark on the road and when it locks in I can see 2 tire marks on the road. I've had lockers before I know its a locker.

alot of those detroits you had to set up first before you could just abuse them

Yeah It might just be messed from the previous owner not setting it up or breaking it in right. IDK I might pull the cover off this week and see if I can find anything.