First, both black wires are ground, but don't wire it there at the socket, there should be another connector that runs both sockets per corner, that is a lot easier to get to.
In the front they are on each side of the fans. In the rear there is a junction block above the spare tire on the left side.
Use a test light to determine which wire is the turn, the other will be your parking light.
Hook your test light ground to any clean non painted metal then probe your wire, like I see you have done.
Turn your lights on and the test light should come on and stay on with parking and will flash for the turn.
Your resistors can be hooked up from either end into the power wire, can't mess that up.
You only need to splice into one wire, but you will have to use two resistors (you have two turn signals in each corner, right?)
Hook two wires from one end of the resistors together and splice into the power wire.
Hook the other two ends together and I would run them to a good ground, you need to mount those resistors
because they will get hot, don't just wrap them with tape to something that will melt or let them dangle.
Don't use those scotch locks...they will cause trouble in the long run, make a good solder joint.
So here's what I did. One end of the resistor has to go to power, the other end goes to ground. It does not matter which end goes where... On the front, I ran two resistors in parallel, two wires down to one and spliced into the 6 pin connectors on each side of the shroud. One wire spliced into the turn signal power wire. The other ends of the 2 resistors, I did the same way, 2 wires into 1, and ran that wire to the body ground located on the firewall. Works great. Mounted my resistors on the inner fender, easy to get to. (See pics below)
I tried to use just one resistor, no go, still hyper flash, you have to use two.
I didn't try to wire them in series, since I found wiring in parallel works.
I found that you really only need one wire going to the connector, the hot side of the turn signal, and the other end of the resistor can be grounded anywhere that is ground, even if you have to make the wire longer to get there. You don't have to wire the ground to the ground wire at the 6 pin connector going to the bulb is what I'm saying. You can, but you don't have to, make it easy on yourself.
One splice for each corner instead of four.
On my 2015
Front left turn 6 pin connector X110 wire was BU/WH
Front right turn 6 pin connector X120 wire was GN/VT
---Check the wiring diagram for your truck !
The right side connector is a pain, you have to remove the air filter box to get to it, and also to replace the bulbs. On both sides you can get to the bulbs through a small opening on the inner fender.
Two resistors for each side, just ran a wire to the right side and spliced into the 6 pin connector over there.
Run the other end of the resistors to the stud.
The same thing can be done for the rear turn signals with two bulbs on each side...there is a junction block just to the left of the spare tire, one wire one splice, then just find a good ground.
Both wires for rear turn lights were D-GN but in different connectors.
Rear left turn junction block X63A connector X2
Rear right turn junction block X63A connector X3
---Check the wiring diagram for your truck !
To get to the rear turn signal bulbs and back up light, you must remove the tail light housing. With the tail gate down you will see 2 screws to remove, then carefully pull the housing straight back.
There are clips on the very end that fit into holes in the bed, that I broke when removing the housing, that are replaceable... GM part # 22876572, good luck.
Rear resistors mounted to reese hitch, single wire to junction box plug. Other end going to ground.
TEST ALL THE BULBS BEFORE YOU INSTALL THEM BACK IN THE HOUSING.
If they do not work take them out of the socket and turn 180 degrees and push back in to the socket and try again. Most LED's are polar.
Resistors mounted front turn signals
Here's a good ground under the hood
Rear resistors mounted.
I made my own "good ground" in the rear. I have some marker lights grounded there also.
Hope this helps.