When I switch on my head lights, my turning lights in the front bumper also light up. The light is very weak but it is on... When I put on the turning signal lever, everything works fine, both sides.
How do I solve this? This is for 70SS El Camino.

check all ground wires to headlights and turn signals.

The park lamps in all cars since 1968 will stay on with the headlight.
Your park lamps coming on with the headlights is normal, and yes it is a weaker light.
The same bulb is used in the tail lights-----taillights are not too bright either.
The brake and turn portion of the lamps is much brighter.

The park lamps in all cars since 1968 will stay on with the headlight.
Your park lamps coming on with the headlights is normal, and yes it is a weaker light.
The same bulb is used in the tail lights-----taillights are not too bright either.
The brake and turn portion of the lamps is much brighter.
Are my park lamps the same as in my turning direction lamps (sorry for maybe incorrect words)?? If you mean my side markers...yes, they work and they use the same 'plug in' bulb as the tail lights. Thats not the issue.

Front light wire harnass is new so that should not be the problem? And to what I know, the turning light housing is not supposed to be grounded in the bumper or does it?

Yes--the front parking lamps also serve as turn indicators.
The front turn indicators will come on with the taillights and stay on when you pull the knob all the out for the headlamps.

Sidemarkers in the front are connected to the park lamps---(are on my pickup anyway)

Just that when they come on-----they appear very dim in the daylight and then not even bright in the dark.

When you turn the turn signals on with the lights on-----they should flash 'bright-dim-bright-dim etc.

When the lights are completely off, they will flash 'bright-off-bright-off.

They will do the same thing that the taillights do

EDIT---since you are in Europe----are you required to have amber REAR turn signals?????----if yes----the taillight comment above will not be right.

And yes----ground the lamp housings to the bumper or any sheetmetal part up front.

In fact, that is the situation now with headlights on: dim-bright-dim-bright...

Oke so what I understand is, that it's correct that the turn indicators in my front bumpers should be on when headlights are on, however very weak? In that case, there is no problem.

For American cars there are exeptions. We can use the original tail lights as turn signals.

In fact, that is the situation now with headlights on: dim-bright-dim-bright...

Oke so what I understand is, that it's correct that the turn indicators in my front bumpers should be on when headlights are on, however very weak? In that case, there is no problem.

For American cars there are exeptions. We can use the original tail lights as turn signals.

Your understanding is correct. I wouldn't call it very weak, but certainly not as bright as when the turn signal is flashing. You will definitely notice a difference between the two.