Hello, I have the same lathe, but no collet closer. I have however seen pictures of one and it's nothing but a long pipe with a hand wheel on one end and threads on the other for a 5C collet. The pipe is passes through the spindle and at the end is the hand wheel to tighten the collet which presses up against the spindle when tightened. The only thing you have to figure out is the total length so the collets pull into the spindle correctly.
Making one has been on my list of things to do, but I just haven't found the time.
Good luck!
Dale P.