No left blinker/stop at 7pin connector

Check it by using your hazard lights. If they flash, the relay is OK and you have a woring issue.

Check the wire grounds where the lens connect to the vehicle. With a test light check to make sure current is arriving at the bulbs. If not, then follow the wires back to the light switches.

you obviously have a short circuit
first disconnect plugs to blinkers try fuse to save on fuses get 12v globe attach two wires and connect were fuse goes if fault still there globe will light
chances of dash small if light shows fault there drop dash and remove globes
i would bet on blinker wiring has chafed and shorted to ground
kevin the electrical doctor

Could be the brake lamp switch is bad , stop lamp fuse 20 amp in under hood fuse box could be blown .Check the fuse ,if not blown check for B+ voltage at the brake switch , location - top of brake pedal under the dash . Do you know how to test automotive electrical circuit's using a DVOM - digital volt ohm meter ? Looking at a wiring diagram so you know which wires to test would be good too . Do you know what a wiring diagram is ? Free ones here http://www.bbbind.com/free-tsb Enter vehicle info. Year , make , model an engine size . Under system click on lighting ,then under subsystem click exterior lighting . Click the search button then the blue link. first diagram top left you will see the stop lamp switch . orange wire in is B+ voltage . Press the brake pedal while checking for B+ coming out on the white wire . No B+ coming out ,replace the switch . Will be other wires as well , other switch etc... check the right one .
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There is a tail lights fuse for the truck, but not for the trailer.
First, check that your left tail light on the truck is working, if not fix the problem (new bulb, bad contact, fuse).
Then the obvious suggestions regarding the trailer are: Check the tail light portion of the bulb to be sure it is not blown. If good (best to put in new one to be sure), then check the wiring from the front of the trailer all of the way to the non working bulb, including every connection and at any place it is secured to the trailer frame. If all is good with the trailer circuit and bulb, then check the truck's trailer connector, including any adapters. If by chance the truck is wired with a flat 4 wire harness the problem may be solved (but usually the blinkers are the problem). Modern trucks require a 5 wire harness which self adapts to the standard 4 wire trailer circuit. Check for dc power (12 volts) from the truck's female connector. One wire will be ground, others will be taillights (turn on headlights), brake lights (have someone press brake pedal), and blinkers (turn on switch and blinkers).

well there could be a couple of things happening here your flasher could be on it's way out, which is on your fuse panel, check your owners manual, or if there is a cover, for which one this is you could have a bad ground, which these our known for or a broken wire or loose wire the best way for someone to try to find this, is when this happens, take a test light or volt meter to back probe the wires to try to find the break in the wire, then trace your ground and make sure it has good contract, if rusted clean up check for cracks, bare spots in any of these wires, if found fix, by splicing wire, using a crimp wire connector, with a heat shrink tubing to protect it, these can be found at an auto parts store also your turn signal switch could be at fault here

It does sound as though the trailer connection is the source of the problem, check to see if the wiring has been resting on the exhaust pipe and melted through, shorting the wires. Also check if it is squashed or damaged anywhere. Failing this you may have to pull the trailer connector apart and see if the wires have come out inside and are touching, this can happen if the trailer connector is pulled hard.

either check for voltage at the blinker and also check for left blinker fuse . NO voltage at connector there is an open in wire replace try to find the open torn insulator or wire being exposed.

Check the plug at the back of the truck for corrosion. The brown wire entering the truck plug should be the the running lights, if no juice at truck plug in, you need to trace it back to the source looking for broken, pinched, wires, or poor connections.

Ok this a way different problem than i thought it was first thing to look at is the relays and fuses and connectors to make sure they are not loose, pull them out and reconnect them. Engine running = vibration. Engine not running = no vibration. If thats good your left light blinker may be shorted to your constant power. Your right blinker may have an intermittent open. I looked at turn signal flashers online they are about $10 each, maybe swap em out then return if it does not fix it. It really sounds like a wiring problem though so look at the back side of where the light is connector and tell me what you find if anything
Good luck