Hi Leevis, nice bike you have there, nd great to find it again after so long.. Very lucky!
If you look at this photo you will see the bolt that holds the brake onto the frame..
Modern bikes and modern brakes have a different way of doing this. A modern caliper brake will have a recessed Allen key bolt that sits inside the frame and looks tidier. Only problem is the hole has to be slightly wider to fit the bolt. Also the caliper rod is shorter. Basically the hole in your frame is too small to fit modern calipers...
The solution is to either use a period part that fits or drill out your precious frame to make the hole bigger or sometimes you can combine modern brakes with old rods.
I have tried all three and more but I wouldn't drill your frame if I were you. maybe if it was some old rusty frame you didnt much care for but this one has some sentimental value right?
personally I think the first option is best and stick with what you have! I ride weinmann 500 on an 80's racer I have, never had any problems, they look nice too.
Here is a photo of a couple of rear brakes to show you the difference..
Hope this helps.. The one on the left is like yours and the one on the right is the newer version..