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No one has found anything concrete so far, but I did find in the original FFIV that encounters are not purely random. Try this: load your recent save and try to get to a specific area as quickly as possible, while noting and running from all the encounters. After that, reload your save and try to follow the same path in the same amount of time. Chances are you will run into at least some of the exact same encounters.
I think the RNG might be seeded by a formula that involves both your game clock (not the actual time) and the amount of steps you've taken (or possibly what tile you're on). The hairy thing about this, though, is that if you were to fight your encounters, you likely won't get the same results with each repeat, though you will get similar results if the battle happens in the same amount of time as the last time you fought it. If you turn on Auto-Battle, you'll notice that your first couple of hits will likely do the same amount of damage each time. However, you should also note that Auto-Battle does not seem to affect the game clock, so whether or not you use it may affect things like drop rate.
It is also notable that if you were to repeat the same encounter using the steps above that the rate of Ambushed, Back Attack, and Pre-emptive Strike will still appear to be also random, but this can probably be attributed to the seed formula using tiny, indiscernible increments of time (although the RNG that governs damage seems to have a much wider margin for timing).
I have also noticed that if you were to go to a new location and enter a battle and then return to the previous floor that the next battle order will be the same as if you had fought on the original floor's prior battle.
I was testing this in Ceodores tale in the mist cave. From my save point, I would enter and the battles were always in the same order.
For many tries I got the same order of monster battles.
One time I decided to enter the challenge dungeon and fought a battle there. Approx the same amount of time as a normal battle would of taken in the previous area. After the battle I exited the challenge dungeon and got into a random battle, which in turn skipped the one battle I would of missed and continued on the same cycle.
1 2 3 4 5 6 7
1 2 3 Ch 5 6 7.
Each attempt I would hard reset.
I did notice though that one time after I had waited a while without running around for a battle the order of monsters did change a bit.
IF we can get enough people working on this, we might be able to come up with a RNG for specific battle orders, though not drops.
found a great spot to try for a stoneblade rng in ceodores cd... hard start last save point before the cd boss...full moon 5 steps down out the door right 5 steps there will be a fight at step 4 run from it 3 steps down your be at the bottom of the stairs 6 steps right your stop at a rock 3 steps down 3 steps up at the rock fight 2 black lizards and 2 iron backs walk back and forth from the stairs to the rock a few times repeat same fight walk back and forth a few more times fight 1 black lizard 2 magma turtles theres 3 chances to get a stoneblade.... ive tried 20 times same fight everytime....both guys are capped at lvl 50 ceodore has mythril sword, shield and helm, plate mail, giants gloves hooded man has mythril sword, shield, armor and gloves, steel helm