OK You're holding half your problem in your hand. Note the smooth face, or the shallow dull teeth ( not sure which from the photo). Note also the lack of serious bite marks on the dropout. If you search imaged of vintage bikes, you'll see dropout faces badly chewed up.
As I said, that's only half. The other half is your hubs axle, which seems to be aluminum. The axle itself doesn't matter, but note the smooth aluminum faces, which are trying to gum your frame because they lack the teeth.
So, new vintage skewer. I also recommend treating the axle. I keep a bottle of nail polish into which added some sand. I clean the axle with acetone, then apply the sand paint and let dry.
The reason for treating is that there's play between the axle and skewer, which will allow the axle to creak under load.
Getting bite from both axle and skewer may be "belt and suspenders", but may be absolutely necessary if you climb steep hills.
__________________
FB
Chain-L site
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