http://www.brandon.ca/images/pdf/bylaws/5463_parts2to3.pdf
Your answers can be found in Section 35 (m) 4 & 5. Looks like the camper is fine if hooked up, but not if left unhooked on the street overnight.
From the link,
35 GENERAL STANDING AND PARKING PROHIBITIONS
Unless specifically required by other provisions of this By-law, or by the direction of an Officer to do otherwise, it shall be an offence for any person to stop, stand or park, as follows:
(m) a truck or other vehicle on a street in any residential area designated and zoned as such under "The City of Brandon Zoning By-law", as amended, between 2200 hours and 0700 hours, where:
(1) the gross vehicle weight of which exceeds 5773 kilograms (12,727 lb.): or
(2) the length of which exceeds 10 metres (32.79 feet) in length alone or in combination with other vehicles attached thereto: or
(3) the vehicle has a passenger capacity, inclusive of the driver thereof, of more than sixteen (16) people: or
(4) the vehicle is a trailer, licensed or unlicensed, and the trailer is disconnected from any other vehicle: and
(5) fifth-wheel recreational trailers, other recreational trailers, motorhomes, and buses which have been converted into motorhomes are exempted from this subsection so long as these recreational vehicles are so parked for less than 48 hours, are unoccupied and, in the case of trailers, are connected to a motor vehicle: