I figured it out. Just drag a message from the Mail app to the Files app on iPadOS and an .eml file of the message will be created.
The key was in the Importing from iOS section of EageFiler’s documentation (emphasis added):
Importing Files
If your EagleFiler library is not stored in the cloud, you can use your iOS device to save files to a folder in iCloud Drive and then import those files either manually or via a script.
If your EagleFiler library is stored in the cloud, there are a variety of apps you can use to create new files. If you save them in your library’s Files folder or To Import folder, they will be automatically imported to the library back on your Mac.
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- The iOS Mail app does not have a Share button, but you can import mail messages by using the Print command to save them as PDF files or (on iPad) by dragging ang dropping the message to the Files app to save them in one of EagleFiler’s folders.
Technically, EaglerFiler does not need to be used at all for this to work. Just dropping it into any location in Files will create the .eml file, which I did not know until now. Now that I have the file, I can store/index it with whatever tool I prefer.
Thanks to everyone for the help.