Juan, in post #5 described a way to tell, by raising the rear of the car. It doesn't confirm if the the viscose coupling is working when one wheel spins, but will indicate if the differential has the coupling built in.
This works because the viscose coupling is supposed to be sealed between the left side gear and the differential housing by rubber seals, in order to prevent mixing of the special silicone oil in the coupling with the gear oil in the rest of the differential. The seals are quite tight -- they can be because for most normal driving, the left side gear and the differential housing turn together, so there isn't a lot of wear. When one wheel loses traction, there will be slippage at the seal surfaces, but only for the time of the slippage. So the seals can last a long time if not abused.
Because the seals are fairly robust and tight, the side gear and differential case are sort of held together by the seal friction. Consequently, when the rear wheels are raised and the transmission is in neutral, turning one rear wheel causes the other wheel to turn in the same direction. (The drive shaft also turns, of course, because the differential case with the crown gear is turning). Similarly, if the drive shaft is held in place (e.g. MT in gear), it will be more difficult to turn one rear wheel (you're fighting the seals) and to the extent it can be turned, the other wheel will turn in the opposite direction. But the drag will be very (!) noticeable.
In a non-LSD differential, when turning one wheel the other turns in the opposite direction and the drive shaft for the most part, doesn't turn, or turns slowly relative to the wheels. (This depends on drag in the opposite wheel. If the brake is binding, the wheel will turn less, and the drive shaft more.) Turning the first wheel is easy provided the brakes are off. Also, if the drive shaft is prevented from turning, it's still easy to spin one wheel while the other turns in the opposite direction. Not so with a viscose coupled LSD.
Again, this can confirm whether or not the differential has a viscose coupling, but it does not confirm if it is actually functioning (i.e. the special fluid becomes more viscose when there is wheel slippage). Also, if the seals happen to be badly worn, the friction might not be as noticeable; but if this is the case, there's a good chance the silicone liquid has already mixed with the gear oil and the coupling isn't working in any case.