One simple test I do on problem trailer lights is to test the hot lead (usually the black wire) with a jumper light. I touch the lead with one light clip and touch the trailer frame with the other jumper wire clip (or probe). If it lights, that tells me I have power.
To re-establish the grounds I identify the ground, remove it, clean the contact point with a method that will not damage the trailer, and reinstall the ground. I use a wire brush on a Dremel tool a lot. My only assumption while repairing trailer wiring is to assume everything is wrong or broken.
With the clearance lights on my Airstream, I replaced all the fixtures with a two wire type light. I attached the hot wire by solder under heat shrink. I added a solder on eye end to the ground wire (usually white or green), and attached it under a new stainless steel attachment screw.
When I worked on the can type rear driving lights, I removed the fixtures, cleaned the lamp sockets with a round wire brush on a Dremel, removed and reattached all the ground wires, removed and replaced all the bulbs, tested each socket with the battery charger and new bulb, cleaned and brushed all the reflectors, replaced all the steel mounting screws with stainless steel screws, and reinstalled the fixtures with all new hand tightened lenses. (I never use a power screw driver on lens cover screws.)
I don't test the whole system until I've performed the above steps on all the lights.
When I rewired the trailer 7-way plug, the grounds were loose and held by wire nuts. The trailer body ground connection was corroded. I twisted all the ground wires together, added a new #10 wire lead, fluxed the twist and soldered the twist with my map gas torch. Then I soldered an eye connector to the new lead and screwed it to the body on a cleaned location with a stainless steel screw.
I diagrammed the 7-way lead wires, added a new fuse panel, and soldered all the connectors to the wires. I used a 7-way tester to wire the trailer 7-way plug. I used the 7-way tester to wire the umbilical cord removable end, and I used the 7-way tester to establish that the tow vehicle was wired correctly and all elements functioned.
A previous owner had removed the breakaway switch lead wires from the 7-way connection point, put wire nuts on both wires, and hid them behind the inside skin panel. I installed a new breakaway switch, and reattached the lead wires.
When I tested the Airstream trailer with the tow vehicle connected, I had the charge line and the backup light leads reversed in the removable cord end. I reversed those two leads in the cord end, and everything worked. My cord is reversible. My trailer is wired to a standard 7-way tow vehicle plug.
A cord that's not reversible tells me something's wrong. If everything's right, the cord has to be reversible.
A standard configuration is important to me because I tow other standard 7-way plug trailers. I have three other trailers, all wired with standard 7-way plugs. A standard configuration is also important to me because I want emergency towing services to be able to plug in and tow my trailers in case of an emergency or breakdown.
Will a miss-wired 7-way work? Sure . . . but why add an element of confusion to something so simple to get right? For me, It's easier to wire it right than to wire it wrong. Anybody can come behind me and diagnose all my wiring to a wiring diagram with no head scratching at all. I can tow my trailers with any tow vehicle with any standard 7-way cord.