How to replace right rear turn signal bulb. doesn't look like I can reach the bulb without removing the entire assembly. Looks like I need a tool that fits on a star head to remove it. Correct?

You simply have a burned out bulb or bulbs. With the key turned on turn on the directional for the left side and then the right side. Typically one bulb is blown and the opposite side works normally. Observe the normal side and note which is the flashing bulb. It is the flashing bulb on the other (malfunctioning) side that needs to be replaced. To replace the bulb you must remove the entire brakelight assembly, which isn't difficult. Open the trunk and locate the electrical harness that lines up with the brakelight assembly. Near the harness, locate the two (possibly three) nuts or wingnuts that attach the brakelight assembly to the car. Once the nuts are removed, the assembly can be pulled off the rear of the car. After replacing the bulb, be sure to test the operation of the new bulb before reassembling everthing.

{: ) REMOVE THE RIGHT FRONT WHEELHOUSE LINER
The wheelhouse liner is sometimes called the mud guard or the splash shield, whatever.
You may remove the right front tire.
-Start removing all those push pins and #7mm screws. No need to remove the entire liner. You may loosen only the half portion, just enough clearance for your arms to reach inside and aim for the rear of the headlamp.
-Reach for the Headlamp Bulb Accessory Cover. Rotate the cover counterclockwise and remove.
-Release the bulb from the headlamp assembly (turn counterclockwise) Disconnect the electrical connector. Just remember the positioning of the bulb so you can swiftly reinstall a new bulb.

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Here's the procedure on how to replace the signal light.

1. Open the trunk
2. If you have a convenience net, remove it.
3. remove the top plastic wingnut that the convenience net hooks to.
4. pull back trunk liner
5. remove the 2 plastic wing nuts found under the trunk liner
6. carefully pull the tail light assembly from the vehicle
7. squeeze the tab on the socket (turn signal lamp in the inboard socket)
8. turn socket counter-clockwise
9. pull out the socket
10. pull lamp straight out
11. push in new bulb
12. reverse steps to reinstall lamp assembly
Note: replacing left and right turn signal bulbs takes about 5 minutes.

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You need to squeeze the little 'fingers' on that white piece to allow the taillamp assembly to be removed. See the YouTube video at the link.
How to remove tail lights in Dodge Avenger 2011 up

You'llhave to raise the rear compartment door fully. Next locat the tailight you wish to replace or same if you are replacing one of the tailigt bulbs. This would include the stop bulb or turn signals etc.
Next there is a black plastice side panel located between the lamp assembly (the entire plastic housing) and the inner portion of the rear compartment door. There you'll see two phillips head screws which you must remove. This releases the entire assembly.
You then next gently give it a small tug toward the left (if a left side assembly) or to the right if other wise. What happens there is that there is a stud that's held pretty snuggly by a modled ring in the body assembly. Don't twist the lamp assembly up or down unless you want to break this off but give it a slight pull outward. Then you're done. The entire assembly will be released and you'll be home free for changing any of the bulbs or even replacing the entire assembly. W/o breaking it of course.

I replaced the front right turn signal on my 2005 Pontiac Montana by reaching up from underneath. I tried removing the battery but the opening from above was too small. I was able to pull the ground effects open enough to get my arm in. When you reach the bulb holder feel for two wings on the bulb socket and give the whole socket a quarter turn to and it will release. The wires are long enough so the entire bulb holder will drop down below the vehicle so you can easily replace the bulb.
Reverse the step to put it back in. You will not be able to see what you are doing so I had someone guide me by watching from above. Took less than 10 minutes once I decided to change the bulb from the bottom. I did not need to jack the vehicle up or use ramps.

Replacing headlamp bulbs
Handle a halogen headlamp bulb carefully
and keep out of children’s reach. Grasp the
bulb only by its plastic base and do not touch the
glass. The oil from your hand could cause the bulb
to break the next time the headlamps are
operated.
If the bulb is accidentally touched, it should be
cleaned with rubbing alcohol before being used.
To remove the headlamp bulb:
1. Make sure headlamp switch is in OFF position,
then open the hood. If you are replacing the driver
side headlamp, unclip the electronic module on the
right side of the battery and move it out of the way.
2. Locate the headlamp bulb through the hole in the
upper radiator support assembly.
3. Release clip and
disconnect the
electrical connector
from the bulb.
4. Remove the bulb
retaining ring by
rotating it
counterclockwise
(when viewed from the
rear) about 1/8 turn to
free it from the bulb socket, and slide the ring off
the plastic base. Keep the ring to retain the new
bulb.
5. With out turning, remove the old bulb from the
lamp assembly by gently pulling it straight out of the
lamp assembly.

To install the new bulb:
1. With the flat side of
the bulb’s plastic base
facing upward, insert
the glass end of the
bulb into the lamp
assembly. You may
need to turn the bulb left or right to align the
grooves in the plastic base with the tabs in the lamp
assembly. When the grooves are aligned, push the
bulb into the lamp assembly until the plastic base
contacts the rear of the lamp assembly.
2. Install the bulb retaining ring over the plastic base
until it contacts the rear of the socket by rotating
clockwise until you feel a “stop.”
3. Install the electrical connector into the rear of the
plastic base until it snaps, locking it into position.
4. Turn the headlamps on and make sure they work
properly. If the headlamp was correctly aligned
before you changed the bulb, you should not need to
align it again.

The tail light assembly might have to be removed to gain easier access to the bulb. The socket to the bulb is mounted to the assembly. The socket usually takes a 1/4 turn to line up the guide pins on the socket for the assembly. The the bulb inside the socket either pulls right out or push down and turn a little to the left. When you purchase a new bulb, then you can tell what type is in it.

Just did this "easy fix" on my 1999 Camry.
Lift trunk lid and pull away carpet covering the tail light. Retain plastic pins that hold carpet in place. Be prepared to have your knuckles scraped by the carpet as you work.
On the 1999 Camry, this was NOT a tool-less fix. You could reach in, turn the tail light socket a quarter turn and them remove it without tools. You then simply pulled the bulb straight out (it was bulb size 904 on my 1999) and plug the new bulb straight in.
NOW... the rub. Although the bulb/socket came out easily, we found it impossible to get the correct angle to replace the bulb and socket without smashing the bulb. Two intelligent adults tried for 30 minutes.
So... step 3. Easy but requires tools. Get your socket set (I couldn't find the right socket, so I used a pair of needlenose vice grips--worked fine). There are two threaded bolts with nuts in the interior access area for all of the light sockets. Unscrew nuts, retain. Now look on the exterior edge of the tail light. There will be one more solid grey nut. Remove and retain.
Step 4: You can now loosen the tail light cover and pull it out enough to allow you to safely insert the bulb/socket assembly. Gently turn it until you can insert the socket, and then give it a quarter turn to lock it in place.
Step 5: Push tail light cover back into place making sure the two interior bolts are in place.
Step 6. Replace and tighten the three nuts.
So, not a 30 second fix. More like 10 minutes. Easy, but a pain, and requires a tool, but truly, if this clumsy 6 months pregnant woman can do it outside in the dark... so can you.

No, you can easily reach your hand behind without removing anything and the bulb can be removed and replaced. If your hand is too large then their are two screws on the top of the light assembly that once removed you can pull the hole assembly out and change the bulb