OK, Lets check your wiring.
For the front turn signals. You have a dual filament bulb. That is OK but you will only use the large filament. I see three wires on each socket. This means only one socket wire will be wired to turn signal for each side. One wire not used and the ground will be attached to good ground place near light. Assuming the black wire is for ground. Socket may ground itself to hood when installed.
The left front T/S lamp large filament wire will be wired to Light blue switch wire. Right front T/S lamp large filament wire will be wired to dark blue switch wire. Each of those will have a companion wire to the dash turn indicator bulb. Either two wires from one terminal or spliced. See diagram.
I checked the wiring. It is as you described. Light blue (blue/white) is the left T/S. Dark blue is the right T/S. The violet wire connects left and right T/S socket. Black wire on each socket will ground to hood or socket housing.
And yes, one light blue (blue/white) and one dark blue wire routes from firewall connector to the dash connector.
If you test bulbs before installing on truck, the sockets/housing MUST BE GROUNDED.
I tested the T/S harness with the flasher and the bulb sockets directly on the battery (+). Sockets were grounded (-). Flasher and bulbs function was perfect.
Rear turn next:
You will use both filaments on each light. One is from the light switch only(small filament) and one from the T/S switch (large filament). Large filament left rear is wired to yellow switch wire. Large filament right rear is wired to dark green switch wire.
Small filaments are spliced together with license light, any way you wish....and they are wired to the headlight switch brown. So three wires going to rear. I usually eliminate the rear connector shown on diagram. This reduces voltage loss, intermittence and possible moisture entry.
It is wired as you describe 
At the moment the wires are connected together with the square orange click connectors
This leaves VIO WHT BLK switch wires.
1. VIO is supplying the flash signal to T/S switch and is wired to fuse panel flasher terminal "L"
OK, I think here is the problem. The L of the flasher is connected to the brown wire. But the fuse panel is wired like the original. I was on this path a few days. Please see post #7. I will post a photo of my fuse panel backside
2. WHT goes to one terminal of brake switch
Correct
3. BLK goes to horn relay.
Correct. Horn works perfect.
4. Other terminal on brake switch goes to headlight switch terminal as shown on diagram. Same terminal as a fused hot. see diagram.
Correct
Of course some wires mentioned may go thru connectors where indicated on diagram.
FIY: When making a turn and at the same time applying brakes, the turn signal switch shuts off the large brake light filament from brake switch power on that side, to allow the large filament to flash. That is why the brake switch is wired to T/S switch.
So now you have work to do. Please advise any questions or difficulties. Check fuses.. some could be blown by previous tests/activity.