Well, here it is:
0.6mm crochet hook on the left, ‘fine’ tambour hook on the right. The tambour hooks come in different sizes and need to be fixed into the wooden holder by tightening the screw. You can see (I hope) that the tambour hook has at least two advantages over the crochet hook: (1) the head is more pointed so it pierces the fabric more easily; (2) the ‘eye’ of the hook is deeper and narrower, giving a better grip on the thread.
This is the design I’m working using the hook. Is it easier with the correct tool as opposed to improvising with a crochet hook? So far, yes, it is. This sample is being worked on dupion silk, which has a much tighter weave than the cotton fabric I used for the first tambour sample. I doubt that the crochet hook would have pierced it effectively. It’s still quite fiddly, and it takes a while to get the hang of it, but I like it very much.
Brief update: I should have mentioned that I got my tambour hooks from here – although you will need to check on the availability of the wooden hook holder as I believe they are difficult to source.