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.
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.