You should sew in your petersham tape between the layers attaching it to the coutil or other lining fabric. Sometimes when using a thin outer fabric the waist tape is attached on the inside of the corset so it lays against the skin when worn.
Firstly I’d like to start by pointing out that a waist band or ‘tape’ is not a necessary corset component; many corset patterns are designed without and this is perfectly acceptable, especially in historic corsets and bodice patterns. A waist tape will however provide added strength to the waist area of the corset pattern which is the part of the garment that takes the most strain when worn. This added strength will often give the waist a more dramatic curve as the tape prevents any stretching of the fabric.
On a corset pattern the waist should be marked, if not the waist band needs to run along the smallest part of the corset, through the narrowest point of each pattern piece. Your waist tape should be made of petersham ribbon, this is a strong unstretchable ribbon and you can tell you have the right stuff from the distinctive ridges on running along the edges. If you look closely you’ll see it’s made from one thick thread that runs back and forth across the width leaving ridges at the edges where it turns back on itself.
This is so it doesn’t show through the outer fabric as a bulge. When you sew on your waist tape make sure to attach it before the bone casing, bone casing has to go on over the top. If you sewed them on the other way round you would be sewing through the casing to attach your waist tape and would not be able to insert your bones. It’s a mistake you only make the once! This also means you won’t be able to use the seam allowance as bone casing so if you plan to do this you’ll have to leave out the waist tape altogether. As mentioned above 18th century corset and bodice patterns didn’t have waist tapes.