As a second year non-law too, my experience is that you cannot apply for most TCs at the moment. I think that you generally apply in your final year. Some firms do allow non-law penultimates onto their vacation schemes, which of course you could try to convert. Other people might be able to tell you if any of these are still open.
I also know that some firms don't allow you to apply for vacation schemes until your final year as a non-law, and then only recruit from that. I'm not sure how that'd work as a non-law grad given you'd have graduated, so I'd appreciate some insight here too.