Hi A,
Don;t know if you still need an answer to this..
I personally would not be happy to leave my car in the car parks at La Linea for anything over a few hours. I DO park in the street (around the main parque) during daylight hours, but again, would only leave my car in a public side street out of the area.
Perhaps contact the airport for ideas? They say there is a parking area actually inside the border - I have seen same - and there is a guard on the gate - but as to the security?
Perhaps - contact Crown Airuga (sp?) the car rental co in Sotogrande and ask if they will do you a deal. Park on their forecourt - pay for one of the staff to drop you off/pick you up on your return.
Their offices are in a nice quiet place away from the madness of La Linea!
Goodluck,
SJ