Depends what equipment you have and how much stringing you need.
If I need 2mm wide stringing line I'll make it 2mm wide but 3mm deep, the top surface can be a rough saw cut as you'll flush it down afterwards with a plane or with a scraper. Therefore I'll bandsaw off a veneer that's about 2.5-3.0mm thick, then I'll pass it through a drum sander to dimension it down to exactly 2.0mm. Then I'll either bandsaw off 3mm wide strips (to give the 2 x 3mm I want) or I'll knife off the strips. 2mm in Ebony is borderline for knifing, it's do-able but I prefer it when I cut off the stringing with a single pass.
Your other option is to buy in stringing ready made from a supplier like this,
I once did a fairly detailed WIP showing how I go about stringing and inlaying, It showed how to plane down stringing lines to a slight wedge shape for a perfect, gap free fit. If you search you might find it.
