Greetings,
That looks like a very nice pen you've got in that CS 12. I think that you'll find the nib to be both very smooth and responsive to your hand - it should glide across paper.
If I remember correctly, the CS 12, 15, and some 70 and 80 series pens were made of casein. I had one and let it soak overnight in water (before I knew better (that's how I learned to know better)) and it went to mush. I think that the pens with the gold veins in them are made of casein.
This means a few things to you. It will warm to your hand and feel more comfortable the longer you use it to write and you do not want to soak it in water

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Congratulations on a wonderful new vintage Conway Stewart. Happy writing.
Peace,
Phroneo