Good question, and I'm in the same stage of remodel...the 110v shore power.
My question is: How is the trailer truly grounded while under 110v shore power?
But I'll try and assist you with what little I do know.
I kept my original breaker box and we photo documented every attachment. My original 30 amp shore power connection had three 10 gage wires running from the exterior female plug to the breaker box; a black, a white and a yellow. The yellow was attached to the interior aluminum skin of the trailer via a ring terminal and metal screw. The black connected to the load side of the breakers using a jumper to hit both breaker busses. The white was attached to the common neutral within the breaker box.
The box was bolted to the interior skin, but the common neutral (white) is actually insulated from the box. It provides a direct neutral across each breaker. I test circuits by attaching a 6v battery using 3ft alligator clips to various wires, leads, etc. Then I trace the circuit using a cheapo voltage meter ($4.99 Harbor Freight). In this case, if I attach one clip to the black wire in and one to the white wire in, I read 6v across the breakers and 6v across the common neutral. But if I move my neg lead to the actual box, I get 0 volts telling me that the box is insulted from the common neutral.
So, I'm guessing that the ground in 1959
was supposed to be via the leveling jacks, or the tongue jack. It might not hurt to carry a ground rod attached via clamp to the frame and just hammer that thing in when you make camp!