We’re very near the end of the Thaumaturge Hunting Log Rank 5 now! The last two items take you into different Garlean Empire strongholds. The first is Cape Westwind. Now, the MSQ brings you here (no spoilers), so if you’ve not visited Cape Westwind yet, maybe hold off on completing the 4th Cohort Hoplomachus entry.
As with other Hoplomachus Garleans elsewhere, you’re looking for sword-and-shield fighters. Start at X:12.4, Y:6.4 and gradually fight your way West. But stay zoomed out to a degree so you can check the nearby enemies for your targets.
As mentioned below, you can go from Horizon. It’s miles away, especially if you can’t fly yet. Alternatively, if you have Vesper Bay Aetheryte Tickets left then using one here will save you a bit of time.