a method of determining which internet server is causing lag

You can find out which server is causing you ffxiv lag by using functions included in windows. This is for analyzing the lag where everything intermittently stops for a couple seconds, not continuous long latency.
TLDR; use dos window, netstat, tracert, ping

Step 1: NETSTAT
Determine the ip of your game server. You might think you already know this, but check anyway. There is some misinformation going around about the ips used. Before you start your game, open a command prompt window. Type netstat. If you want to save the info you can type it like
Netstat > c:\temp\filename.txt
But the temp folder has to already exist. Create it if necessary. You can use any folder, but you cant just use the root. Now login to the game – all the way in. Tab out to the dos window and do the netstat again. You should see a few new lines almost at the end, like so:
TCP (deleted for privacy) 199.91.189.33:55028 ESTABLISHED
That 3rd field is the game server I use – NA normal. Ignore the :55028.
Now you know your ip.

Step 2: TRACERT
In the dos window type
Tracert 199.91.189.33
Or whatever your server ip was that you found in step 1. Or optionally you can use
Tracert 199.91.189.33 > c:\temp\tracert.txt
to save the data to file. This shows the path your data uses to get to the game server. Any one of those hops could be causing your lag. If there is a timeout in the list just ignore it for now. Print this out.

Step 3: PING
Now you can determine which of those hops is causing the lag. Start at the 5th hop (you can start anywhere but best to pick somewhere in the middle or a little earlier). Type
Ping –t ip
Don’t use the > redirect this time because the t makes this continuous output and you want it onscreen. Play your game and when you get one of those freezes tab out to the dos window and check. If the last couple lines show timeout then either this hop is doing it, or one of the earlier hops is. If you got a positive then hit cntl-c to stop the ping, and repeat it for hop #4. Eventually you will find the cutoff where every hop previous does not timeout and every hop after does. That’s the one that is causing problems.

Note:
Remember that ping timeouts can occur separately from game lag. Servers typically assign lower priority to ping requests, so pings (and tracerts) may occasionally show timeouts when the game is not lagging at all. You need to wait till there is game freeze and then check if the ping timed out as well.