Sticky: 2008 Outlook XR RH Turn Signal Failure
 

I have a 2008 Outlook XR with the same problem, also around the same time, while in transit, the interior lights came on, Courtesy Lamps. Pulling the fuse under the glove box for the Courtesy Lamps turned off the cabin lights, but each overhead light is wired with separate power so you can turn on each lamp with the button.
The directional signals all pass through the Body Control Module, BCM, under the dash next to the brake pedal arm.
The BCM detects no load to the front lamps, so then flashes the lamps you do have rapidly, after 3 cycles at normal speed. This emulates the old bimetal flashers that need a certain load to flash at normal speed. If you have a lamp go out, then the flashers cycle fast, and you know you have a lamp out.
Well I jumped the gun and bought 2 new lamps for the right front turn signal, $50, and no fix. Also the lamps on the mirror are out.
The circuit that feeds the right front and the mirror lamps (LEDs) is all one circuit that ties together near the fuse block in the engine compartment.
The source of the circuit looks like it is directly from the BCM, Wire 1315 D-BU/WH from Plug X4 Pin 5.
The relays on my 2008XR under the hood, one for left and one for right, are for the rear directional lamps, those may only come with the Trailer Towing Package that this is equipped with.
No fuse after front left & right are split.
Getting ready to see if I can find the wires under the dash.
This model has lots of trouble with loose connectors and contacts in the plugs, I can fix many problems by moving wire harness components around.

2008 Outlook XR RH Turn Signal Failure
 

Well it turns out there is an error in the internal circuits of the BCM, Body Control Module.
If you pull the Courtesy Lamp Fuse, such as you might do when your Headlight Switch fails, keeping a live signal to the Courtesy Lamp Override input to the BCM, running down your battery if you don't notice,
The Right Hand Front Signal Lights do not operate, nor do the directional lamps on the RH Mirror work.
Put the fuse back in, everything works fine.
The right rear signal blinks normally 3 times, then rapid blinks because it doesn't see the load of the front lights.
It doesn't see the load, because when the BCM was designed, someone used the Courtesy Lamp power source to also feed the front turn signal indicators.
(whether on purpose due to other mistakes, or just muffed it)
For you deep trouble shooters, the front lamps (pair) draw 3.35 amperes, the front mirror LEDs draw 0.3 amperes, or ~ 3.7 amperes all together.

Front Turn Signal Wirirng 2008 Outlook XR
 

A little more information on the routing of the front turn signal wires.
The Dk Blue/White 1mm wire from X4-5 on the (Body Control Module) BCM routes to the under hood fuse box (RH Side), to a connector bolted to the bottom of the fuse block X2, on the firewall side. From that same connector, the Dk Blue-Wh wire that feeds the RH Mirror LEDs loops back.
Within the bottom of the under hood fuse block is a system of jumpers and bus bars that route this signal to Connector X1, the connector that is toward the front of the vehicle, and towards the right wheel.
The connectors unbolt with two large Phillips head screws in the middle of the fuse block, unsnap the 7 impossible to reach latches around the perimeter, to get access to these plugs.
A paper clip from the BCM connector shunting power from pin 1 (Red/White +12V) to pin 5 on X4 easily tests the body harness wiring. The BCM will trap your key in the ignition if not all plugs are connected up.
Connector X1 separates from Connector X3 with the release of another small plastic latch between the two, the two slide apart vertically.

Awesome! Thank you for coming back and posting such detailed troubleshooting information.

Now a sticky!

Think you're the first member under 10 posts to ever "earn" a sticky in my 14 yrs as mod here.