My friend Michael Fuchs (son of Ernst Fuchs) draws also with a ballpoint pen, but he is using a Mont Blanc - his results are amazing. They are expensive, but you might get a refill that fits into a less expensive pen. The refills don't cost that much (compared to their pens! - i.e. it's like buying a battery for a Rolex watch) and are superior quality: non-clogging, light-fast etc and perfect control with shading, soft and hard strokes.
PS: it may be good if you did a shape-search drawing with a pencil first to establish the body.
Recommended book (that's the way I learned decades ago: Nicolaides: The Natural Way to Draw - link is to my Google Drive cloud file.