I have a number of external Ids in my SFDC environment, but I can't see them in the Data Loader or in the Jitterbit Data Loader.
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Are the fields actually on the account record? Maybe an obvious question but it's easy to overlook the obvious and would explain what's going on here; also double check that you've not got a sandbox/production mismatch.
I don't think FLS is the issue as I'm pretty sure you'd still see the field name etc. via the API, you just wouldn't have access to data inside it.