Your clearance lamps and brake/turn signal lamps should work with no battery installed. Those lines are direct connects from your tow vehicle to your trailer; they don't go through the converter (your outside trailer vehicle lights (not the porch light) are powered by your tow vehicle with no trailer fuses involved, your tow vehicle provides the fused connections for those lights) or your battery to operate. More likely you have a broken wire somewhere, or a bad ground. If you have power from your truck's #3 pin, then the trailer's wiring is at fault. If you don't have power at the truck's #3 pin, then the truck's wiring is at fault. You would have to check the 7 pin connector on the trailer for continuity if the truck is actually ok. It may be possible ( I don't know how you "tested" your truck's pin out power) that your truck isn't providing the power. Many vehicles made since the development of "computer" control (CAN Bus) are not set up for towing if the vehicle did not come from the factory with the "tow package". For instance, if you bought a Jeep Grand Cherokee without the tow package and added your own hitch and 7 pin connector, the connector would not function properly. You would also have to add two relays and a fuse in the under-hood distribution panel in order to actually have light and brake power for the trailer...
Your interior lighting may or may not work with no battery installed no matter what your truck's output is. Some converters require a battery as a "filter" for passing current to your trailer's interior lights so, interior lights, unless you know your converter's ability, is not going to be a good test...
My 2 cents, your mileage may vary...
2 Cats; J-Lo and Ragamuffin :R
2014 Thor Tuscany 40RX DP
2011 Ram 2500 Longhorn CTD HO
2011 Keystone Cougar 318SAB (now gone)
2008 FunFinder X 210WBS (Sadly gone)