If it is a LQ trailer it will be running off of the trailers power then thru the truck.....  If it is a NON LQ trailer it will run directly off of the trucks power.  On my LQ trailer I installed one on the center of the rear and one on the curb side and I have them on 1 switch on the rear post so they both are on at the same time.  On our little trailer I have one on each side and the curb side switch is in my tack room and the street side switch in on the rear post hooked into my horse compartment light switch.   Most of the time horse trailers are wired with a hot from the truck so you can run power to load lights.  I will fish around in the hole you found and you will more than likely find a wire for this.  Sounds like someone just cut it short and left it.

Any trailer can be powered by a stand alone battery or powered from most towing vehicles. If there is no trailer battery installed, one can easily be added and run on a dead loss system, whilst being recharged only when needed, or a power wire can be drawn from the B+ lead of the towing vehicle. If the dressing room of a non lQ equipped trailer has a shore cord for AC units, it can also be used for charging purposes with a converter.

A stand alone trailer battery has advantages over utilising a towing vehicle's power source. One is that some trucks cannot provide B+ power until it is physically running. To overcome this requirement, some owners by pass the interlock system to enable a draw without a running engine. If a mistake is made, you can end up with a dead battery and no starting, if an appliance is inadvertently left on. Another advantage is if the trailer is disconnected from the towing vehicle, you still have your lighting source.

We have a LQ trailer that has both systems. The LQ's and stall lights are powered from its own battery, which is recharged when an AC source is applied. We can walk up to the stored trailer and use its lighting without needing a truck's power. A solar power source offers a trickle recharging. During the winter, a battery maintenance unit is utilised.

With a change out to LED bulbs, a single generic "marine battery" will last a long time between the needs of being recharged. If sporadic lighting is your only concern and doesn't involve running other items, the installation of a battery is not an involved process.

Update:  Lights are working.  They tapped into the backup light wire (white) of the trailer light wiring harness, which isn't used for backup lights, to power them from the Deep Cycle battery.  They didn't work until I located a poor connection at the positive feed wire coming off of the deep cycle battery at a twist cap connector.  Now looking at installing three switches in the tack area to separate the left, right, and rear exterior working lights.  This should reduce the load of having four lights on at a time and extend battery time.

Thanks all!