1. Obain a Tyco Piggyback flat car. They are readily available on eBay. This one is currently listed - $1.99, no bids yet. You will see what is special about this car in Step 3.
2. Remove the trailers.
3. Remove the yellow decking. It will not be used. It snaps into slots (arrow) in the chassis so it is easy to remove by poking the tabs up from underneath. This is the "exploded view". The slots make mounting a camera easy.
4. I left the stock weight strip in place, and added an additional cast weight from a scrap F7A engine, securing it with a mini-zip tie through the slots. This makes the car very stable when moving. (Without it, the car wobbled a lot) The two white pieces are leftover from a wire shelving install. The J-hook on left is hot glued in place. The other piece is mini-zip tied through the slots, and it can slide back and forth to snug up against the camera.
5. Place the GoPro in position and snug it up. Push it along with your loco. Watch your clearances - if you have tracks on 2" centers, it will strike anything on an adjacent track.
Here is another approach by modeler Jim Booth. Jim writes "A mini video camera available dirt cheap at Wallymart. Comes with a clip so it fits on the end of a gondola. Perhaps not as clear as a Go-Pro but does the job. And it is the same width or a little less than the rail car. Camera cost me $44 in Canada. Think it's around $24 or so in the US."