In what circumstances can foreign amateur radio operators, other than United States citizens, operate while visiting Canada?

For a visiting amateur radio operator (other than a US citizen) to operate in Canada, there must be a reciprocal operating agreement between Canada and the visitor's home country. Additionally, they must obtain the appropriate authorization or permit prior to transmitting. Citizens of the United States have a special automatic reciprocal agreement with Canada and do not need a separate permit, which is why the question explicitly excludes them. Operators from other nations do not enjoy this automatic, permit-free privilege. Options suggesting automatic global ITU privileges or automatic Canadian grants are incorrect. International operation almost always requires specific bilateral agreements and formal permits.