A general principle of insurance is that you can't insure anything which you don't have a financial interest in. (So, for example, I can't take out insurance against my neighbour's garden shed being blown down, as I wouldn't lose any money if that happened).
So you need to consider who would have to bear the loss if the mechanic's tools were stolen and neither of you had any insurance. I suspect that it would be the mechanic, meaning that he needs to insure them.
However if there's a contractual arrangement between you and the mechanic which means that he could successfully sue you for compensation if his tools were stolen, then it's you who needs the insurance cover.