I think in both Gaius's case and, how
Archbishop Thordan in Heavensward
, both might have seemed beguiled by the Ascians, but it appears both actually thought that they could defeat them after they had outlived their usefulness (after all,
Thordan all but told the player this, bending the truth that he was "paying lip service" to the Ascians' promises of alliance when in actual fact he was already working with them.
Basically they both were horribly misguided, they really did believe they had the power to defeat the Ascians themselves - of course we knew differently, but to be fair to both of them, we did have the benefit of foresight truly knowing what the Ascians were like, that they were the actual ones behind Primals in the first place (given the fact the Ascians were going around Eorzea under the guise of the 'Paragons' to the beast tribes and teaching them how to summon their gods), and then just happened to show up to them and plonk 'amazing means' of sealing/controlling Primals into their hands (Ultima Weapon and Azys Lla respectively - not surprising how both were ancient Allagan devices).
Not to let Gaius and entirely off the hook of course though, but such knowledge was really known only to Minfilia and those in her organization (the Path of the Twelve pre-Calamity and it's successor the Scions of the Seventh Dawn), and thus us by extension - either way, Gaius and were practically pawns in a sick chess game where they thought they were actually the players.