Is the turn signal flasher relay an open or closed circuit

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

When the ignition switch is in the RUN or the START position, voltage is applied through the TURN/LPS fuse to the normally closed contacts of the hazard switch. A single flasher in the hazard switch performs the following functions:
• The turn signal operation
• The hazard flasher operation
When the turn signal switch is in the LEFT position, voltage is applied to the following components:
• The left turn indicator
• The left front park/turn lamp
• The left rear turn lamp
The lamps immediately turn on and flash as the flasher opens and closes the circuit. If a bulb is in need of replacement, the turn lamps will flash at twice the normal rate.
Without testing i would probably say the flasher is bad .
do the four ways work ?

Did you check the dash fuse block? fuse #12?
also maybe the brake fuse.

needs flasher relay which is the 4 way flasher

Turn on the Durango and check each of the four turn signals to make sure that the bulbs are not burned out. If you find one that has gone out, replace the bulb and retest the turn signals. When a bulb goes bad on this circuit, the resulting operation can mimic a bad flasher or one that is failing.

Locate the combination turn signal flasher and relay. It is on the left end of the driver's dash. Open the access door and view the collection of relays and fuses. At the left side of the mounting block is a larger flasher and relay. This is the combination turn signal flasher and relay.

Test the relay by placing you finger on the relay housing and activating the turn signal. If you have found the right one, you should feel a clicking as the turn signal blinks. Remove the relay, replace with the new relay and close the access door

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Start the Durango and activate the turn signals to check that they each work. The light should turn on and should blink. Also, check the hazard lights to make sure they work.

okay...the signal fuse powers horns, dash indicator lights (neutral, OD etc)
so all that is working fine?

the other common items are the wiring to the bulbs and the bulbs....doubt all 4 failed at once.

Looking at my wiring diagram, it looks like the system was designed so the hazard circuit and the turn signal circuit cannot be used at the same time, It appears that the common component to accomplish this is the Hazard Relay (not Hazard Flasher Relay). Basically the power to your Turn Signal flasher is fed from the Hazard Relay if your Hazard Switch is off, and when the Hazard Switch is ON, the Hazard Relay switches and cuts off power supply to Turn Signal flasher, and feeds the 4 turn signals for 4 way flashing.
So I suspect possibly either your connector at the Hazard Relay is loose, or the relay has failed
I'll try to find location for you, looking for a 6 wire connector with the following colours
Brown/White, Brown, Brown/Red, Brown/Green, Chocolate, Dark Green.

It may be under the right side cover....there is one flasher relay there...but will do some research.
You realize the Venture has a 5 year warranty?

First of all check the Flasher relay.The other to check is the ground wiring.Is the wiring's proper or getting short.The flasher is clicking in off position this indicates that its actually turning off.the flasher is still receiving any current to function. so the wiring's needs to be checked and confirmed.The wiring procedure  in 1999 GMC sierra  is as follows:--
The circuit is fairly simple: 12 V power from the ignition relay is brought to the Hazard switch. In the Off position, the 12 v is routed through the Hazard switch to one pin of the flasher. Another pin of the flasher goes to ground. The third pin goes to the turn signal switch, where it is connected to either the left or right signal light circuits. The other side of each bulb is connected to ground. When either the turn signal or Hazard switch is turned on, the current through the flasher causes it open and close its internal contact in the 12 V line, thereby turning the signal lights on and off. So, for the flasher to continue to click when the ignition switch is at ON/OFF (assuming there is no clicking when it is OFF), there must be a connection from the 12 V supply through the flasher and the turn switch. It is possible that there is a wire between the flasher and the turn signal switch that is worn and contacting ground.
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the hazard switch above the radio is your problem. if you put on your signals and they don't flash turn hazards on then off and they will flash. (changing this *** will fix your problem

On the pass. side beside the glove box (when open) there is the fuse box. above or beside the fuse box is the relays for the turn & hazard signals.
You may have to remove the glove compartment all the way over to the ash tray that whole assembly comes out look up where the glove compartment used to be. You will see the relays. Use your owners manual it will point you to the flasher relay.
If your turn signal is not flashing, replacing the flasher or relay might not fix it. Especially if one side flashes and the other doesn't, there is probably a short or corroded wire somewhere in the circuit. Refer to a wiring diagram to test with a test light. 
Good Luck and hope this helps

Hi,

If I understand you right based on your post/description, the signal lights would still turn on even if any or both of the flasher relays are removed. Should this be the case, then the signal lights are not getting the power from the flasher relays but from the brake light circuit.

Perhaps your concern is not with any of the flasher, but simply missing or loose ground more particularly with the rear lights. Perhaps you could try determining which of the wires for the brake lights and signal lights (as they come out of the light assembly) would be ground . A test and even possibly a temporary workaround is to hard wire a second ground connection from the determined ground wire of the lights and attach it to any conveniently located bolt or screw to the body. it may be to your advantage to do this on all the rear lights assembly.

Hope this be of initial help/idea. Pls post back how things turned up or should you need additional information.

Good luck and kind regards. Thank you for using FixYa.