Congratulations, you have a GM Corporate 10-bolt.
You should be able to get a locker, limited slip or spool fairly easily.
There are a few different ring gear sizes in the 10-bolt diffs, you'll probably need to pull the cover and use a tape.
-edit-
Nevermind, you said dual wheels. Definately not a conventional 10-bolt rear.
Does it also have a drop-out carrier like a Ford 9"?
You have an Eaton axle, the GM RPO code will be H072.
The H072 should have a bolt on the snout of the diff with a locknut. This bolt has a bronze tip and runs against the back of the ring gear to prevent deflection.
They came with factory lockers but they're hard to find now. Gearsets were usually 4:10 and 4:56.
Tough as nails but parts are getting hard to find. Apparently Corporate 14-bolt guts will fit but I've never tried it myself.
More info:
http://www.ringpinion.com/DiffDetails.aspx?DiffID=225&SearchMode=Diff&Type...
http://www.ringpinion.com/DiffDetails.aspx?DiffID=226&SearchMode=Diff&Type...
Shawn