Long story short, dust builds up in the turn signal and causes problems with the contacts. It's also possible that the turn signal relay is bad. This is more likely to cause a loss of turn signals. It can be repaired by removing the relay cover and cleaning any corrosion off the contacts. For support on this topic, refer to this forum thread.
The turn signal relay is also the hazard switch relay. Replacement is shown at the bottom of the page.
On a side note, the car's horn started having some occasional small beeps in left hand turns the week before. A quick blast of compressed air behind the airbag while turning the wheel fixed that.
Here is a video showing what the clicking is like.
The mk5 generation switch should have fixed this problem by closing the area
around the base of the switch and adding another cover. Your mk4 switch
has some open space where dust can enter. For illustration, below is the
mk5 part. Not only is there a ring trim, the base of the stalk extends
under the trim and should keep dust out.
torx or allen wrench
electrical contact cleaner
10mm wrench to disconnect battery
T12 triple square bit for removing the steering wheel
First disconnect the negative terminal on the battery, turn the car on, and step on the brakes a few times. This will discharge any stored electricity. When handling the airbags, always touch a bare metal ground before touching the airbag to discharge any static electricity and wear a grounding strap! See the TOS Agreement for the full legal disclaimer.
The quick and easy way to fix this is to use some compressed air or no-residue electrical contact spray to clean the area around the base of the turn signal. Move the switch around and spray the cleaner into the base of the switch. This often works so try it first. At worst it's a temporary solution or doesn't work.
If it doesn't work you have to take the switch apart. First remove the airbag and steering wheel. See 1000q: mk4 steering wheel removal or 1000q: mk5 steering wheel removal if you are doing this on a mk5 car. Make sure to mark the bolt to the steering column so that the steering wheel isn't put back crooked. The mk5 had a stamp on the shaft that lined up with the wheel but the mk4 Passat didn't.
Do not rotate the circular thing that the airbag plugs into. This is called the clockspring because it has a ribbon cable wound inside like a spring. This is how the wires maintain contact as the steering wheel rotates. If you rotate the clockspring the ribbon cable inside will be too short in one direction when you put the wheel back on.
Remove the steering column trim. The upper arrows show the location of
2 short phillips screws. The middle arrows show the 2 long screws.
There's also an allen head or torx bolt on the bottom-rear of the lower trim.
If you have a mk4 you don't have to completely remove the lower trim - just
let it hang down. If you have a mk5 the upper trim is attached with a
flexible flap - just set it aside.
Remove the clockspring. It's held on by some small plastic clips.
Bend them back slightly to release it. You can unplug it or let it hang to
the side. Also remove the single allen or torx bolt that's clamping the
turn signal and wiper ring onto the steering column (yellow arrow). Here
you can see the kind of dust build up around the base of the turn signal stalk.
It should look like this before you pull the stalks off.
The "clip" has a single lock that you press to unlock the
plug. The "2 clip" has an upper and lower lock that you pry off
the lock tab to release. Pull the other plugs off by their plugs.
Never pull on the wires.
If you can figure out how to get the clips off from the rear, you can just remove the 4x T10 torx screws on the front indicated below to remove the cover instead of removing all the plugs and loosening the assembly.
The dark red arrow is pointing to the canceling switch that springs the turn
signal back to center when you're done turning. Click the turn signal up
or down and then press the switch to see how it moves for proper
reassembly. Remove the 4x T10 torx screws and use a very thin screwdriver
from the back of the switch to release the 2 clips on the left side of the
Remove the cover and note the other white plastic switch. This is the
high/lower beam selector. Note how it sits in the turn signal
groove. The yellow arrow is pointing to a hole where the canceling switch
pivots. There's also a tab on the upper cover where it sits. Then
just gently lift the turn signal up and clean the contacts.
Installation is the reverse of removal. Just make sure you check the turn signal lever for proper movement before putting it back. Also check the high/low beam switch for proper operation. In my case, while trying to pry the clip off from the back of the assembly, I pried the base of the copper lever which operates the high/low switch, visible at the upper left. This caused no high beam. I ended up taking the switch apart and bending the base a little to restore the contacts.
Torque the steering wheel to 37 ft-lb. The bolt should only be reused 5 times.
It's possible that the hazard switch/turn signal relay is causing the problem. These can also fail and cause the turn signal to not operate.
First slide the radio out and to the side. If you have a mk4, use the
radio removal keys and the radio easily slides out. Don't try to pry it
out and don't unplug it. Then press the metal retaining clips in and push
the switch out.