Signal and hazard light not functioning

Well this is not a US market car, so I do not have any access to specifics on it. But I would say that it is probably related to a part called a flasher (basically a relay). The flasher makes the clicking sound and operates the necessary lights when powered. But if something is causing it to burn out, they probably do need to go through the wiring, as something likely is wrong there.

Being as new as it is and under warranty like it is, I would suggest demanding a loaner vehicle. At least here in the US, they will give you something to drive when they are going to have your car for that long.

I will second the "let them fix it". Especially as it is electrical. Think of it this way, they do the repair and something shorts out and fries the ECU or burns up the wiring, they pay to repair/replace it.

Now if you trace it out and repair it, and the problem is something else that fries the ECU or worse burns the wiring or car, you get to buy a new car because you are not the authorized repair shop.

Normally the dealer wants to do as little as possible to repair a vehicle, for them to state they need to trace the wiring and the ECU means it probably is not a simple "pop out the bad part and install a new one" repair.
I have spent a day tracing out a short in a vehicle, and discovered it had burnt off a lot of insulation on wires around it.