Many of the very early production cars, typically with VIN's ending in 000500-001000, used a slightly different manual transmission than the rest of the DeLorean production.
Most DeLorean cars with manual transmissions use the 369-08 unit, identifiable by the 21 spline clutch disc. If the transmission is still attached to the engine, identification is done by checking the small round metal tag attached to the transmission end cover as shown.
The other, earlier, transmission has a model number of 369-03, and is most easily identified by having a 10-spline clutch disc. Like the other unit, if you don't have the clutch out of the car, you can identify this transmission using the model number, which can be found on a round metal tag, attached to the transmission end cover.