Does it have to be in the contract, or in the customer salable drawing, or somewhere? Or is just "common sense"?
In my company we design and manufacture several automotive components, for example, harnesses and stereos. I would assume that the stereo is not "product safety", but the harness?
I looked for the definition of the term and couldn't not find anything.
There is no universal rules for safety of all products. Safety requirements for some products are defined by legislation or CE mark, or by customer requirements. It is not common to define requirement for product safety in contracts, simply because such requirements are implied. Or, it can be part of customer requirements as requirement for raw materials to be used or features of the product to be demonstrated.
In you case the product safety can be demonstrated by providing attestation of safety of raw materials or by testing durability of t he product (harness) on strain or other product features. Basically, you need to demonstrate that your product is safe for use and fit for its purpose and, maybe, you can consult your customer on how to demonstrate this.