Electronic – the connector on kinesis keyboard board called

I'd strongly recommend sending Keytronic an email on this one. They're one of the few who will know for sure without disassembling and reverse engineering what you already have. They'd probably be thrilled to hear from such a fan of their work!

I went through something similar with a heavy IBM tactile keyboard from 1984. The cable unplugged on both ends and was lost in a move, so I was looking for the pinout of their slightly squashed RJ19 looking connector. It was manufactured by Lexmark, and they helped sort me out via email after routing me to their 'old man on the mountain' keyboard guy. Sadly, it died it's final death about a year later from a close encounter with a four year old. I still hit the thrift stores once in a while looking for another to pop up, but I've pretty much adjusted to my $9-on-sale keyboard now.

I've dug up the schematics of the T60 keyboard as well as the X41. There is a very high chance that the keyboard receptacle is AA01B-S040VA1 manufactured by JAE. The landing pattern is the same and it looks very much the same (Google images for the 30 pins version: AA01B-S030VA1)

Molex SlimStack 54363-0478 can be used as a substitute to the AA01B-S040VA1. My previous edits say otherwise because of my bad soldering. After fixing the soldering, it works well.