Unfortunately your chances of getting actual mechanicing work part time at 16 is slim.
You will get work in an autoparts shop, , but as close to a workshop you owuld get is being the **** kicker who sweeps floors etc unless you took on an apprenticeship.
THOUGH, Theres no harm in going around and ask local mechanics if they would be prepared on hiring you part time so you get experience. At work we have a young kid come in and does alot of the jobs none of us can no longer be bothered with, he loves it, he learns and it gives us a break from doing notorious ****, but I work in IT so its a bit different