Imagine if you will if Gilgamesh were in fact a dungeon boss in his very own dungeon, what would he do, what would he use? In my opinion, he would kind of be like the Absolute Virtue of FFXIV. Able to use any and all job abilities/spells, but not at the same time. Let's go through a series of phases shall we?
Phase 1
He'll start off with the Naginata, here he will use some DRG abilities(Jumps, Dragonfire Dive) and some of his own unique ones. This phase will last until 80-75% then he enters phase 2.
Phase 2
He now has four arms active, he will wield 4 different weapons that will change in each encounter you have with him effectively making him almost a different fight every time depending what combination he is using. He will also do a quadruple auto attack effectively attacking with all four weapons at the same time.
Excalipoor Will hit his target for 1 damage
Masamune A channeled aoe in melee range where he will deal massive damage to those in range
Zantetsuken The same as Odin's current incarnation in the game. Instant death to everyone, only way to avoid this is running away and LOS'ng him(He'll just sit there and cast it within let's say.. 5-10 seconds)
Buster Sword He will use Blade Dance on his current target. Dealing heavy damage.
Excalibur Will do group wide aoe damage that's rather flashy and just as blinding as Holy itself is.
Revolver(We already have gunblades, so why the hell not?) Randomly targets player, charges them, melees with said weapon and "may" crit if he manages to press the RB button*Cough*(He'll have somewhat of a decent chance to crit with the ability, albeit not for much using a whole boom animation) He'll target ranged jobs with this more often.
These will be his unique abilities, he has every other job ability/spells as well and may wield one of the current relic weapons. Likesay, he wields Zantesuken and Masamune along with Thyrus and Curtana. He now has WHM and PLD abilities/spells. He will have these up until 50% when phase 3 starts.
Phase 3 Now here's the fun part! He now has 8 arms effectively wielding 8 weapons to ruin your day. His auto attack is now an 8 fold attack. He will now wield an extra one of his specialty weapons along with more relic weapons adding more abilities to his arsenal. He stays like this up until his defeat in which he retreats into a dimensional void leaving behind goodies for you.
The battle itself could have a newer version Clash on the Big Bridge or use 12's version. It'd be an 8 man emphasizing on using the two tanks to swap tanking roles every now and then during certain ability sets, such as him using Blade Dance. During the entirety of the fight he will say cheesy one liners, especially when he kills a party member effectively mocking and berating you because you failed at avoiding something.
As for his drops, he could drop Genji armor, some of his weapons, such as the Naginata for DRG, Excalipoor for PLD(It'd do rather bland damage, but have very good defensive stats).
Of course, this is just what I'd want to see. Granted the relic weapons are just kinda placeholders to me, SE would probably think of something else to kind of hint what set of jobs is currently using. The entire basis of the fight is to introduce a challenging battle that is not always the same, as every encounter will be different with him. Different weapons, different abilities. It will either be moderately difficult, or DEAR GOD WHO THOUGHT OF THIS SHIT!? Type of fight. Just think of all the fun and rage you would have. Plus all the tears of those who can't beat him flooding the forums saying he's too hard and needs a nerf.