Unlike Baja, ASO doesn't make this a very easy race to chase. When I first went with Darren Skilton in 2010 there was a sizeable group of motorcycles following the race from town to town. This year I hardly saw any of that. I believe (don't quote me) that it cost Klaus about $3k each way to ship his 4Runner. Plus he is without the vehicle for over a month on each end of the trip.
You could rent a truck locally and fly in with your camping gear, I think that would be the best way to go. On a route like this year I would follow the race north to the border, then go to Salta for a few days and chill out. One of the biggest bummers of following the race is all of the spectacular natural and cultural opportunities that we drive past to get to the next location.
Spectator locations are located at:
Zonas espectadores: Dakar
You could go to those and watch some race cars, then follow them on the liaison. Stopping at the gas stations is crazy and cool at the same time. Huge crowds and people asking for photos, hats, t-shirts. You can't get into the bivouac without being smuggled in, but I think that one or two trips to the bivouac is enough to get a feel for how it works.
In the past I've had friends fly down to Buenos Aires for scrutineering and follow the first stage or two, then head home. This makes a nice vacation and gives you a taste of the race without making a huge commitment with limited knowledge of what you are getting it to.