OK
More questions.
Are you using the trailer frame for the ground? Run a separate wire to each light fixture to do the grounding with copper wire not painted steel.
But if you are only getting 8.5V going into the converter then it is less likely to be a trailer problem. But, bad grounds on a trailer can cause a lot of weird seemingly unrelated symptoms.
As mentioned above, hook up a battery charger and try it again.
If that does not fix it, then you may have a bad connection on the bike somewhere.