In case it is helpful, reviving an old thread here with an alternate short term solution that will work for those with a Mk4 Jetta that has this issue (failure of the high/lowbeam switch in the turn signal stalk resulting in loss of low beam headlights).
Note that this only applies if the above scenario is in fact the source of the problem, rather than some other issue like failed bulbs, grounds, fuses, or headlight switch. The scenario is that DRLs and highbeams still work normally on both sides, but both low beam headlights go out when you turn the light switch from off to on, due to failed low beam contacts in the headlight hi/low beam column stalk.
The proper repair of course is to replace the turn signal stalk assy, but I had this happen the other day, needed the car to not be down, and did not have time to order and wait for a switch nor pull off the airbag and steering wheel to replace it etc.
You can get low beams working normally again in about 1 minute with this workaround:
1) Remove the headlight switch on left side of dash (push in, turn, pull out -- watch YouTube if you don't already know how) and unplug its connector
2) Using a VW pin removal tool (or a substitute, with a little more difficulty), extract the female terminal from position #3 in the connector (this is the DRL wire, corresponding to "TFL" pin on the switch)
3) Move this terminal a few spaces over to the empty #7 position in the connector and re-insert it securely there. This corresponds to the 56* labeled pin in the headlight switch, which receives power when you turn the lights on. It is normally not used in Jettas and only in Golfs/Passats etc where there is a separate low beam section of the headlamp. Moving the wire over here puts this unused terminal temporarily to work operating the low beams in the Jetta rather than the DRLs.
4) Plug the headlight switch back in and re-insert it into the dash. You're done.
What this accomplishes is it activates the low-beam headlights when you turn the switch, energizing them via the DRL changeover relay rather than through the column stalk contacts which get bypassed. Essentially instead of running the DRLs with the switch in the "off" position, it tells them them to run in "on" instead, along with the rest of the running lights. This means you don't have DRLs anymore, although most of us don't want them anyway. It also means that if you have the parking brake on your low beam headlights won't work, but that's not much of a problem.
Highbeams will still work normally in this scenario, BUT when you turn on the highbeams it won't cut power to the low beams like it normally would. IMO this is the only thing that makes this suitable only as a temporary solution rather than permanent. Running both high and low filaments in the bulb for long periods of time will generate excess heat and likely damage bulbs or housings. This is best used for folks who need their low beams working again but rarely need their high beams. If extended use of the highbeams is needed you need to either fix the problem properly with a new column stalk and not pursue this workaround, or add a defeat circuit to disable the DRL relay when running highbeams so that they only operate one at a time.
This temporary fix is reversible if you do it for now and then later replace the stalk. Just move that same terminal from #7 back to its original #3 position. You will regain the DRLs if you want them, and the function of the lighting circuits will go back to normal.
Good luck, maybe this will help someone out of a bind if this failure occurs at a bad place or time where you can't fix it right away.