Kurt already showed the basic answer above.
I had measured the size of them on my 1967 Starfire IV (and since I am in Europe in millimeters), they are only about
7.5 mm long, 1.2 mm diameter nails with 2.5 mm head size.
So the head diameter is about double the pin diameter.
2.5mm is about 0.1"
1.2mm is about 0.049".
7.5mm is about 19/64"
You basically need to look for small nails with a 2.5mm diameter head that is round, the length of the nail is not important, you can always file them shorter.
Such nails with round heads are used for upholstery or shoemaking for instance.
Sometimes they are called "Dome head nails" or "Round head nails" ("round" but not "rounded head").
The correct term for such a nail is: "
Escutcheon pin".
You obviously need to find the right size, hre is just one example:
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Ralf