First, let's examine the truck owner's liability. As the truck owner, he is probably not liable for permitted dirver's negligence. As the owner said, this was the first the tortfesor driving his truck. There are two ways that the owner could be held liable. One is that the tortfeasor was employed by the owner to do his business, in which, for any employee's negligence within the scope of the employment the owner is vicariously liable. The second way is that when the owner knew or should have known the guy borrowing his truck did not have a license.
Driving without a license is a crime, but probably not the proximate cause of your property injury. It is only a strict liability crime (negligence per se) and states enacted such a law just for regulation purposes, not for preventing any car accident. Unless when your state legislature enacted the license statute to prevent such harm, it is not foreseeable, hence, not the proximate cause of the injur. Under the circumstances you can only sue the tortfeasor for ordinary negligence, not negligence per se. Which means that, the guy, with or without license, have to use reasonable care when driving on the road and if he breached that duty, it would be your basis to sue.
States will require that you clear the intersection in yellow light. If you see a yellow light but still decide to drive through, most courts will find comparative negligence on your side and reduce recovery, unless you are in one of four states, NC, SC, MD, or VA, that a slight fault of yours will completely bar recovery.
In my opinion you may eventually get some recovery from the truck owner's insurance company if it takes the view that the owner is vicariously liable. If not, you may have to go to the court to sue both the owner and the driver.