1) Yes I read your post and wrote a reasonably comprehensive answer to your no start problem
2) the wiring diagram I found does not show a B & W wire either but does show a 2 terminal seat switch
3) Husqvarna is known for making changes to their wiring , sending out dealers updates but not changing the printed owners manual
3) Husqvarna is the only company that fits the and tamper switches & I have found them on mowers and not shown in the wiring diagrams
5) Yes I have read the manuals, done the trade courses got the certificates and run a repair business
6) here are a lot of people who come here where English is their 2nd 3rd 4th or 5 th language so they may or may not understand what is being aid to them
7) you are there with the mower I am around 10,000 miles away so it is a bit hard to see your mower from here
8) yes I looked at the wiring diagrams in fact I checked 11 of them looking for that B & W wire . however I can read & understand them it would appear that you have difficulties or you would have seen that the lap bar switches & seat switch & brake switches & PTO switch are all connected to one another via the brown wire which is connected to the magneto kill wire ( although that is not shown past the engine pig tail )
9) you got the mower second hand with faulty wiring & replaced the key switch , without trying to do any diagnosis, we have no idea if you bought the correct switch or not as you did not post the numbers nor do we know if any or all of the switches fitted are right or wrong as the switches come both NO & NC and on more than one occasion I have found an owners bought the cheapest of two switches which of course was wrong .
However as I do have manners and do not impose where I am not wanted then I shall wish you all the very best & happy mowing