There are usually practice tests online. In fact, in Florida, I think they can take their permit test online. So, at least you could see if that has anything to do with his reluctance. I would want to find the reason. Most kids are chomping at the bit to get the permit and more importantly the license. You will want to help him with any worry he might have about driving, the test, or just the idea of so much responsibility and independence. Maybe he is thinking about it in more depth than most. There really is a LOT to consider but most just think -- "YES I get to drive!" But he may have a particular worry about driving itself. Best to find out what it is and offer your help. I would start by finding time when you can ask him privately about his concerns. If he doesn't open up, you may have to try to offer some possible reasons and then try to cover them even if he doesn't claim a particular fear or concern.
Has he been shy or timid in any other things? Was he eager to start school, begin, middle and high schools? Is he interesting in dating? Some just are a little less happy with change of any kind. Does he know of any older friend that had a bad accident? Has he ever been in an accident with someone else driving? The fear of an accident can be a big deterrant to wanting to drive. My grandma did not want to learn, but my encouraged her and taught her. In the first month with her license, she was sitting at a red light and someone came from behind and hit her. It was not a bad accident, but it was enough, that she did not want to ever drive again and she didn't. But it could be something entirely different so better to find out from your son what is on his mind.
As much as it does help to have another driver in the family, I found I missed driving mine around. Those were our catch-up times, to hear about their day and what plans they had. Once they started driving on their own, it was hard to pin them down for conversations, especially during each sport season! My youngest was into everything, so getting any chunk of time with him on a consistent basis was tough after he started driving himself. It still is! So maybe you don't want to rush him too much.
Good luck!