The Garmin camera that came with the trailer always has power supplied to it so you can switch on the display at any time. I often have done it to see if the person I am traveling with is still behind me or I have lost them although you would think it would be hard to lose a trailer of this size
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An aftermarket camera could be configured however you want (i.e. find a constant 12v source or wire it into the reverse light circuit - the latter is probably a little harder to find on a trailer that is already built out).
Dave