OK, have just been through this exercise as the result of an auto sparky using a pocket knife to strip away the sleeve on the trailer wires, but that's a whole nuther story.
The checks to do are;
Test each light individually using a fully charged battery (my 14.4V cordless drill battery works a treat.
Ensure that the white is attached to the -VE terminal and then just touch each of the others to check a result, brown for tail, red for brake, yellow/green indicators.
The set of Trojan lights I have just fitted had a brown & brown/white which determined which way the number plate lights point
Check if the clearance lights have been spliced in down near the taillights, the scotchlocks (I hate them!!) that were used on mine were left exposed to water and had turned the copper to copper sulphate or like.
Check that the sheath is sealed all the way to the lights and not damaged, if it is split and there is damage to the insulation, same scenario as above.
Check the plugs near the lights if you have them, do a continuity test on the loom if you have plugs.
Test the lights by jumping wires from a battery to the plug pins, use the continuity test on the loom to determine which pin is earth.
If this all fails, then get a new set of lights.
Repco have the Trojan submersible led lights with 9 Metres of wire attached for $140 with a trailer lock thrown in at the moment.
The lights are cast in resin, and sealed where the loom enters, and appear to be well designed.
I ran separate feeds for the clearance lights loops back to the rar of the trailer to make for easy replacement in case of damage (provides a heap of slack wire to reuse, its only $2 a metre). My first loading incident was to have the chine run along the wire on the top of the mudguard and tear off the clearance light.
Leave plenty of spare wire when running through the trailer sections, try putting a loop in each section, if you damage in the future you have enough to cut and join easily.
For the joins on top of the mudguards for the clearance lights, I soldered the connections, used glue lined heatshrink and then a sheath of heatshrink over both joins filled with marine silastic before shrinking.
The Trojan lights work on my Subaru which can be fussy about trailer light load on the indicator circuits.
I will provide an update after the 25th, coz they will be getting dunked 10 days in a row ;^)