I think we've all hit upon parts of the proper answer.
Early cars used ATF Dexron IIIE. This is a ~7 cSt viscosity product (roughly an SAE 20) with lots of additives for anti-wear, proper friction, oxidation protection, etc. When the transmission got hot, the "rattle" when in neutral was objectionable, so Dodge moved to a 75W-85W product. That is not a typo, the Castrol Syntorq is truly a 75W-85W, even though the Dodge bottle says 75W-80. In any case, such an oil is only an SAE 30-ish grade, so everyone thinking they got something much thicker - surprise!
The Syntorq / Mopar fluid is GL-4 NOT NOT GL-5. Do not use gear oil. Hypoid gear additives are extremely aggressive and not suitable for manual transmissions. GL-4 = T-56. GL-5 = Dana rear.
Because of syncho material compatibility, early T-56's that used ATF aren't supposed to use the thicker oil, but later T-56's can use either. In fact, I think the newest T-56 went back to ATF. This is again a reminder that it's the additives that count, not just the viscosity (thickness.)
For frugal-minded, regular driving, a normal ATF (maybe a synthetic ATF if you want a step up) would be acceptable for any model year T-56. The ATF will shift better when cold, shift fine when warmed up and might rattle in neutral. The 75W-85W will shift a little harder when cold, be fine when warm, be quiet in neutral.
I advocate visiting your Viper-friendly Dodge dealer. If you can't find that combination of Viper-friendly and Dodge dealer, then go to the GM dealer and ask about their Synthetic Manual Transmission fluid as used by the Corvette T-56. It won't say Castrol on the outside, but guess what's on the inside...
The hint from Dave was the "NV4500" in small print on the bottom left. That would be the NV-4500 transfer case in Dodge 4WD trucks that also use the Castrol Syntorq fluid.
Finally, the quantity. My service and owners manual say 4 qts, but somewhere it says fill to the fill hole. So you have to raise the car on 4 jacks, be more or less level, and fill until it won't hold any more. It will be somewhat less than 4 quarts.