Funny story: I met the previous owner of one of mine.
I started a correspondence with the gent, named Egon - now deceased - and traded a couple letters. My initial letter was in German, but he spoke English.
Then, when the economy was down and the dollar bought a lot of euros, circa 2005 IIRC, I went on a ski trip with my sister to Austria*, and flew into Zurich, Switzerland. We rented a car and drove about an hour out of our way to his village. He was waiting for us on a swinging bench on his front porch. Eager to offer some homemade schnapps.
Egon never fought, but served in the early 1960's. The K31 was issued to him new. He certainly recounted his skiing, marching, and freezing nights spent in the mountains with the rifle. Another anecdote was that they have miles and miles of bunker networks in which they'd essentially march in circles. After his active service he was a reservist (they had a term I don't recall), and kept the rifle in his closet with a case of GP11. However, he couldn't break the seal on the ammo. I forget when he said it happened, but when he got old and infirm his doctor essentially reported it to the Army and they came and collected the rifle and untouched ammo. That was the last he thought of it until he got my letter years later.
OP, Good luck connecting!
*:We stayed in a 5 star place for under $200 a night, and since the State owns the mountains and not private resorts like in the USA, lift tickets are like $20/day. Great food + beer too.