Is there a simple setup to use Wireshark to track server connections?

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You should be able to capture the SMTP traffic by installing and using Wireshark on the system that's using Thunderbird. SMTP uses a number of TCP ports, 25 for unencrypted traffic, 465, 587 & possibly 2525 for encrypted traffic, althoguh other ports may be used.

To capture this traffic, determine which interface is being used on the capturing PC by looking at the list of adaptors under the "Capture" heading (probably WiFi or Ethernet), select that interface and then in the Capture Filter edit field enter a filter such as tcp and (port 25 or port 465 or port 587 or port 2525) and then hit "enter".