I had a remote solar panel that was mounted on top of my carport, then there was about 15 feet of wire going to a spotlight connected to the small storage battery beneath the carport. It was motion activated. I used this for about 4 years until I sold the house. It did exactly what you are looking to do, and stayed on for about 30 seconds after I left the area. I did not park here, but I did pass through this area when taking out the trash or moving tools into the utility room off the carport.

Now I have two 15 watt solar panels and a full sized deep cycle battery that will provide power for my 12 x 16 foot garden shed. My DH frequently works late in the shed, since he puts up his tools in there after dark. The shed is a barn style roof with half of the roof facing south and is perfectly oriented for the solar panels. I think we could also run a small fan off this large battery (big enough to run the cabin lights on a boat), and I know that the boat supply store sells such fans. Our setup here is not motion detecting though. Incidentally, I bought both of the solar panels from the boating supply store too.