All 4wd wranglers are capable of being dinghy towed. You simply place the transfer case in neutral, and unlock the steering wheel on pre 2010's. Some time around 2010 on up the steering lock was eliminated.
Manual or automatic doesn't matter. Either one you just put the transfer case in neutral.
So install your tow bar, taillight wiring of choice and go. It's the simplest vehicle out there to dinghy tow. Preferably you will also install some type of braking system due to it's weight, especially with a JKU.
Motorhome users refer to the vehicle towed behind them as a dinghy or as a toad. It's just some of the RV lingo, like some things Jeep have different names like JK or JKU. The average driver doesn't know the difference, to them it's just a Jeep.
The OP is refering to a transmission pump. Some vehicles can be towed but require an auxillary transmission pump to keep fluid circulating through the automatic trans while the engine is off but the vehicle is in tow in neutral. This prevents the transmission from burning up during tow. No 4X4 Jeep requires this.
'13 JKUR 10th Anniversary
Billet, Red int., auto, 4:10, Towed behind motorhome
'12 Ram 2500 Laramie, Cummins H.O.
'09 Dodge Charger Daytona, 1 of 400
Several Antique and pro-tour cars