Fuse for Trailer lights on a '97 v-8 LTD Jeep Grand Cherokee

I'm so sorry it has taken me so long to research this topic and respond to you. I was busy prepping for and getting surgery on my left shoulder.

Here is what I can suggest. Get yourself a cheapo multi tester, or test light for 12V systems.
On the car side, you said it was round to flat adaptor. Replace that piece. Most are made so cheap they wont last 1k miles, some ont work out of the box.
Get another short piece that plugs into that adaptor too.
Using the white wire as ground, like you already figured out, you need to do a little testing.
Ill be back in a while with specifics to test.

Here is your test.

If all of your vehicle lights work, just trailer having problems, test in following manor.
White wire, strip end bare, this will be your common wire, as it is ground.
Clip alagator clip of test light to white wire, with no lights on, probe all other wires, no volage = ok
Turn on parking lights, Probe brown wire. Voltage = ok. Turn off lights
Have assistant push brake. Probe yellow and green, both should have voltage. Probe brown No voltage. Have assistant let off brake.
Turn on ignition, Left turn on- probe Yellow. Intermitant volts good, steady or no volts bad
Right turn- Probe Green. Intermitant voltage good, steady or no volt bad.

IF all vehicle lights work, but no or bad signals on vehicle to trailer connector, replace vehicle side of trailer harness. They sell plugin kits for most vehicles, so no splice required. If all test fine on test harness, re-wire trailer using following as refrence.
Green = Right stop/turn
Yellow = Left stop/turn
Brown = side/rear marker/tail/licence plate
white = Ground to trailer.

This vehicle didnt have seperate fuses for trailer lights. If the aftermarket harness did have fuses, they are VERY close to the connector.

If this helpped you, please leave me positive feedback. It took a lot out of me researching and typing this all one handed.