A traveler carrying a Refugee Travel Document may — quite reasonably — not wish to show a passport from the traveler's country of origin. However, all the Timatic portals I've seen require one to enter a specific country for the traveler's citizenship. A Refugee Travel Document, of course, is not evidence of or an assertion of citizenship in the issuing country.
My experience with the portals mentioned above is that without entering a country of citizenship, Timatic doesn't return a report. Thus my question: how does one complete entering data for a refugee into Timatic so as to generate a report?