Trail driving Pico del Tiede Volcano, Tenerife?

We have just booked a week in Tenerife staying on the West slope of the Pico del Tiede, hooray!
Going to be hiring one of these to get about in. It would be nice to use it head up to the volcano base avoiding the tourist areas over on the East side by using the dust trails on the West that I can see on flashearth and then walk when the trail runs out.
Anyone been there? Know if the trails are possible or if they are private/restricted access? It is a National park after all so I expect there are restrictions If it is restricted, are they gated or can we sneek up without being noticed?
Are there any 'must see' things in the South of the Island
Any pointers appreciated

Not sure about Tenerife, but on Lanzarote the volcanic parts of the island was a national park and restricted access, even the pre-arranged tours had restricted access and could'nt drive the buses on certain road, i think the restrictions are being rigorously enforced due to all the developements (residentual and hotels)going on on all of the islands, But i am sure someone more knowledgable will give you a better answer than me

Last time I went there the crater contained an army firing range. don't know if it's still there though.