For the Thaumaturges (and Black Mages), the 2nd Cohort Signifier is your opposite number in the Garlean Empire. You’ll find them – or more likely they’ll find you – in Castrum Occidens in Eastern La Noscea. The Empire has posted Signifiers high up, a bit like archer sentries. And there are loads of them too!
Get your fizz-bangs on for Eorzea. Start at around X26.0, Y:21.0 and head East into the Castrum. Have fun wreaking havoc, adventurer.