4-way car connector to 7-way trailer connector

I bought a CURT custom wiring harness that plugs into vehicle tail light assembly to provide a 4-way flat socket. It has a simple plug & play design that eliminates the need for cutting and splicing of the car’s original harness. It provides a wire for left turn/stop, a wire for right turn/stop, a wire for tail/side markers/license plate, and the 4th wire for the ground.
Basically this 4-way socket was supposed to be used as in the diagram provided.

The problem is that I am supposed to hook that socket into a trailer with a 7-way socket (ISO 1724).

Usually I am trying to avoid buying stuff that/if I can make as a DIY project.

Obviously I can bridge few of those 4-way socket wires to the 7-way socket:

• the white ground goes to the ground (pin #3 on the 7-way socket)
• the brown tail/license/side markers goes to the brown/black (pin #5 and #7 on the 7-way socket)
• the green right signal/stop light goes to green (pin #4 on the 7-way socket)
• the yellow left signal/stop light goes to the yellow (pin #1 on the 7-way signal)

So far so good. But what about the brake lights?

The 4-way provided assembly seems to use the same bulbs, both for turn signal and brake lights. So when the car wants to signal it probably sends a intermittent voltage through that wire, thus blinking. When the car brakes it sends a continuous (non-intermittent) voltage through that wire to the same common-shared bulb (so we interpret that as “the brake/stop light”, because it does not blink). This make me think that with a 4-way wiring you cannot have both, the turn signal and break light at the same time, because these 2 functions share a common wire/bulb (as I said earlier, is the car that simulates these functions via intermittent/continuous voltage applied to the wire).

The 7-way socket (see ISO 1724) has a separate pin for brakes/stop lamps: the red pin #6.

So basically, the problem I have is to find how to connect the green/yellow wires from the 4-way socket to the pin #6 on the 7-way connector.

If we assume that we just take the yellow/green from the 4-way socket and to link them to the pin #6 it would mean that (1) the turn signal will behave like the emergency lights and nonetheless the stop lamps will do the same and (2) while braking both the turn signal lamps and the brake lamps will light.

OK, instead of using both the green/yellow 4-way harness wires to hook them to the pin #6 (brake) on the 7-way socket I could use a single one (let’s say the Right). This means that while I am using the left turn signal it would be OK, while using the right turn it will flash both the right turn signal lamp but also the stop lights (which will look like the emergency lights). So this option is not working as well.

I don’t see any simple solution (a wiring solution) to the problem above. The only way I know it will work is by the means of an electronic circuit that will take the advantage of the fact that the turn signal has a is intermittent voltage while the stop lights has a continuous voltage.

Any idea/hint/tips that could help me take the fog from my eyes?
Thanks in advance for (1) you patience and (2) for your help.