Santi: Hmm................ I'm not sure how your LED headlights are meant to work and maybe my confusion is because I happen to live on an island near Antarctica - where water flows in the opposite direction down a drain!
However, below is my understanding of how the OEM headlight connectors on Golf mk7.5s for North America Region (NAR) models are terminated. I also include for reference a picture of the pin-out for the BCM.
In regard to "
it should be Pin10/T10 to P13/T14" - yes!
For your question "
15a is equal to KL15a" - KL means Klemme = Terminal/Clamp. So, "
15a" is really "Terminal 15", or "T15" - which is the same as "KL 15a". These are terms that are defined in the industry Standard
DIN72552 - look it up, it's a really good read

and you will find the other terms in your table in the document like "
KL49" & "
KL56a".
But I don't understand why you propose "
i use Pin1/T10 for Pin8/T14"! Pin8/14 is used on OEM headlights for the DRL signal when the headlight fittings do NOT have DRL Modules. I'm happy to be corrected - but AFAIK where the DRL Module is present - Pin8/14 is NOT used . Is
pin #8 on the 14 x pin connector on your physical headlight fittings populated with an actual wire and do the fittings have DRL modules?
For the
15a power supply (which is a switched +12Volt supply with ignition-ON) - the connection is Pin1/T10 to Pin4/T14 - I think!
Don