I could be wrong but I believe it would also be 'Engine' then the housewatchman would have to specify who the run is for. As to having multiple people in the housewatch, there would only be one person on watch at a time, regardless of how many companies. Although, I am not sure how the housewatch rotation works when another (temporary) company is in quarters. Being that they are a visitor, do they have to do the watch at all? Perhaps someone can provide some further clarification to me and FDNYSI's questions.