I'm leaving this post here in case others experience a similar problem in the future.

I've been having this issue the past few days with a fresh client install. Every 5 seconds my client would seem to skip a few frames or briefly seize up. The effect was pretty jarring, so I spent more than a few hours interrogating Google for the answer.

Finally I found this post: https://forums.geforce.com/default/topic/457765/pc-games/ffxi-freezing-every-10-seconds/post/3739662/#3739662

I disabled all gamepad support through the FFXI Configuration dialog as suggested and my stuttering has gone away completely. Not only that, the client as a whole seems to be much more responsive.