If you have an AT then keep it out of Overdrive and you may want to engage the 4 wheel drive just to give you more power at your wheels. if you have a MT then you will have enough power just keep it out of 6th gear. As far as your E-locker goes you can only engage that when you are in Low-lock other wise it will not work.
So if you have an AT just keep it out of overdrive that should be fine for towing keeping it out of overdrive lets your engine work at a higher RPM without shifting up so it wont work as hard, and if you feel that it is still lagging then you can put it in 4hi, but locking the diff wont do anything unless you are in low at which point you wont be able to drive about 18mph. I think the truck is rated at 6500lbs towing anyways so you should be good.
With the 4 wheels engaged, you probably wont even feel the trailer behind you!! A whole lot more control in my opinion.
I need to correct some inaccuracies before someone breaks something...
The FJ Cruiser is rated for 5000# towing - I've witnessed more, but you will end up over GCWR (gross combined weight rating) and if you get pulled over or in an accident, don't be surprised if your insurance goes bye-bye and the nice officer puts you in cuffs...
Towing: I've got 70,000+ miles on the FJ Cruiser I'm sitting in right now (pulled over on I-40 in N-Texas) - these miles were put on in the past 14 months wheeling every weekend and towing a 3000# trailer during the week...I let the truck work between 4th and OD all the time with the automatic transmission, and have had zero issues. (I suggest NOT using cruise control however....easier to manage and improved mileage since it trans is less to auto-shift into 3rd on long/steep climbs). I travel 'within 5mph' of the posted speed limit, and the limit in W Texas is 80mph....again, zero issues. The trailer DOES have electric brakes and we use Tekonsha Prodigy controllers....BIG fan, highly recommended (I have two at home as well)
I've engaged 4-H only a few times while towing, and only while at lower speeds...these have been in low-traction situations like sand and snow where forward progress in 2-H wasn't easy/possible.
Engaging 4-H with an AT _WILL_ bind the 4wd system and _WILL_ likely cause something to give, most likely breaking the transfer case.
Engaging High-Lock with the MT _WILL_ bind the 4wd system and _WILL_ likely cause something to give, most likely breaking the transfer case.
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Top end in 4-L with the AT is over 45mph....yes, I'm a professional offroad driver, and yes, it was a closed course

Find my 'skiing at 49* north' pics in the Trail Rides corner for proof....that yellow FJC is the same one I'm sitting in now....