You can't not have your own taste, it's within you. Whatever you are motivated to pursue, that's your taste. The thing to develop is the confidence to pursue it.
I think that, by definition, what this means is going to be someone different for everyone. For me it meant actively working on problems that interested me and in a style that interested me, even when it seemed like the effort might not pay off.
I was in a similar position, although I was given a more specific topic at first. I was forced to follow my own interests because of my complete inability to do anything that does not sufficiently motivate me. It ended up working out well, which I do chalk up to my good taste haha.
I think a lot of it comes down to learning to tease apart what you want to do because you are driven to vs what you feel expected to do. For example, the way I like to do maths is different to the way a lot of people around me like to do maths, and that caused me to avoid doing it my way because I felt like it was wrong. Now I've learned to embrace my style more (it helps that I've got some good results now), although I still keep an eye out for ways I could improve.