The proposed route for the next section of the North-South highway has been published for 45 days days of public consultation. Map is here
http://www.gobiernodecanarias.org/copt/documentacion/viaria/inf_publica/pc_ptoCaldereta/DOC_2/1_Situacion.pdf
The plan includes dualling the Rosario bypass, with new routes north and south. From the positioning of the southern end it look as if the plan is to continue it inland to the west of the army camp and then probably to the west of chipmunk mountain.
It will be great when it is finished - in about 20 years if the previous section is anything to go by.
much more detailed maps and other stuff here
http://www.gobiernodecanarias.org/copt/participacion_ciudadana/Exp_infra_viaria/pt_prosario_caldereta.html
Out of all this lot which document has a detailed plan of the route?
second one down