To echo what Hog Wild said, the ASO does not make this very fan friendly at all. The first year I went with Darren Skilton (2010) there were quite a few adventure motorcycle tours following the rally. When I went in 2016, there were none. My understanding is that ASO put a stop to that, which seems kind of dumb to me (but it isn't my race).
I think that the easiest thing to do would be to go down to the start and check out scrutineering, and then follow the first couple stages before returning to the start city. You could see some of the race through the publicized checkpoints and potentially even get a pass to get into the bivouac if you talk to the right people. Chasing the entire race is not really that much fun (trust me).
1) VIP Dakar tours. You need to email a dedicated person at ASO and they have these VIP offers. Probably damn expensive.
2) Photographers offer space in their cars if they have free space. Dont really quote me on it but around 8'000 Euros is what you will spend + probably need to pay for Media pass (else I dont see how you can get in to the bivouac) + whatever personal expenses you will have out of the box if you want a dry martini in the middle of the night in Peru or somewhere. They follow the route and go offroad for photo opportunities. Maryan Chitka was looking for someone this year to fill 1 empty space. Even if you are not a photographer its fine, only thing is you will need to live with their schedule and with how they want to cover the race.
3) Find someone who can offer you an opportunity to work for them at Dakar - from wrenching to a pair of spare hands. Happens with privateers.
4) Rent a place if a T5 support truck. Some teams offer that if you want to see the "dark side". I think Boucou assistance do.