Now for the tailstock you can only used plywood sandwiched together (I used a hardwood center piece). The different color pieces you see in the pictures are only for visual clearance purposes only.
The 3/4 plywood pieces overall dimensions are 15cm (6") wide, 21.5cm (8.5") tall, and have the same T-shape cut as the headstock. The angle cut for the two edged pieces is from 22-25 degrees not important. There's a hole on the top that its center is in perfect alignment with the drill chuck's center. Two screw-down threaded inserts are used here for better security, one on each tower. A threaded rod goes through them with its end grinded to a fine point which will help to hold the work-piece in place. The rod is about 180cm (7") long.
At the front end of the rod there's a Coupling nut screwed on, that prevents the turning work-piece to sleep deeper into the point, and also acts as an outer locking stop. In the centre of the threaded rod and between the tailstock's towers there's locking stop nut that can be tight to the left side.
In the inside face of the two towers there's another plywood piece which is identical to the tower but without the angle area. The center width of that piece is 5cm (2") so when you look at it "stand alone" has a cross shape. These two pieces have also the same matching hole on the top. I strongly recommend that you drill the tower's holes at the same time on your drill press.
The center wood piece of the tailstock, is either a piece of hardwood or two 3/4 plywood glued together and cut in a cross shape. The height is not important as long as you leave space to the rod locking nut to be tightened with a wrench. The center wood also provides enough area for the two hold down knobs to hold the tailstock from moving.
Finally at the end of the threaded rod I made a simple hand-wheel to move the rod in and out thus holding the turning piece tight in its position. The hand-wheel is made out of two plywood sandwiched circles 12cm (4.7") diameter, has a wooden dowel handle and is threaded on to the rod with the help of countersink nuts and epoxy.