Eddie might come under closer scrutiny by customs officers than usual, because he lives in one country, has bought his bike in a second country, and is planning to enter a third country.
To a customs official, Eddie would appear to have more reason than normal to sell his bike in the third country, because he did not go to the trouble of shipping the vehicle from his country of residence. Thus, the customs dudes might want some assurance that he will export the bike from the 3rd country - and this leads us down the path to Carnets, which we all know and love.
He could make the situation look less unusual by having an address in the 2nd country, where the bike is purchased and registered, and having a driver's licence from the 2nd country. At least this would make it look like he has some residential ties there, and is likely to return to the 2nd country with the motorcycle.