Should I get rid of my car to get a car I have wanted for a long time?

I currently have a 2004 Ford F-150 which I put a down payment on and my parents are in charge of the payments. I have had the truck for about a year. My parents got me the truck as my birthday gift for when I turned 17. I currently work at a fast food restraunt making $10.50 an hour. My parents financed the truck for 3 years but I have always gave them some money aswell to finish paying the truck faster which should be fully paid off in about a year if we keep paying for than our monthly payment. My question is I really want another car because the truck wastes too much gas I get around 14 mpg and I don't need a truck I want a smaller car for about $10k my question is should I finish paying the truck off and then get another car or have my parents cosign with me for the car I want I'm now out of high school about to start college.

How to convince my parents to let me buy a truck

I'm 16, they are gifting me the truck that my sister used befor me, a 2008 Ford F-150. It has 250xxx kilometres, lots of dents, and electric issues. I have some money saved up and am looking at buying a 1981 dodge d150, which has 85xxx kilometres, and is in much better condition. How can I reason with them to let me purchase my own vehicle, I will have to pay the insurance either way.