I think you're mixing two different processes. - right-clicking a message and clicking 'save as' does allow eml and text and html

 but 

- for pdf output, you need to click File>Save Selected Messages

Both options are presented by Thunderbird...

Right-click, then "Save Selected Messages" shows a list of different formats & one of those is pdf. But it doesn't produce anything.

File..."Save Selected Messages" shows the very same list of formats (and of course one of them is pdf). But it also doesn't produce anything

re :Save Selected Messages

That option will only be visible if you have installed an addon extension called 'ImportExportTools NG' It is not available in the standard release version.

Please make sure you are using an up date version of 'ImportExportTools NG' which is compatible with the version of Thunderbird. I'm using Thunderbird 102.3.3 and addon 'ImportExportTools NG' 12.0.1 This version 12.0.1 does have a fix for 'Save to PDF' for *nix platforms.

When I select an email and use the right click > save selected message > pdf format I get two pop ups: the first is a warning about pdf cannot be imported back - do you want to continue the second is a warning that attachments are not saved - do you want to continue Then a window opens which wants me to choose a suitable folder as the destination for these pdfs, so I choose a folder which I've created on my desktop then I click on 'Select Folder' If I then go to that desktop folder and see what it contains there is a pdf file.

I am using the latest version 12.0.1, and have also posted a request for help in the addons forum.

When I try to save as pdf I do not get the warnings; just the "select the destination directory" In that window, the option is "open" rather than "Select folder". When I click "open" the window disappears, but no pdf file shows up in the folder.

re :When I try to save as pdf I do not get the warnings;

It is possible you used it before and selected the checkboxes to not show in future.

re :In that window...."select the destination directory", the option is "open" rather than "Select folder".

That is odd. Open is used to open file or upload a file. Where are you trying to save it ?

Please choose something very simple to test. Create afolder on the desktop called Test then repeat the trying to save as pdf in that 'Test' folder.

If you still get the 'Open' not 'Select Fodler' option: uninstall that addon, then restart Thunderbird and finally get a fresh install of ImportExportTools NG.

Got an answer from the addon developer:

Unfortunately they don't have an actual "forum" so I just sed the comments. Good news is the dev has a fix!

https://addons.thunderbird.net/en-US/thunderbird/addon/importexporttools-ng/reviews/1170423/