Only parts sold via an Vauxhall Franchised Dealer will come with a 12 month manufactures warranty. This covers against manufactures defects in workmanship/ materials. There are a number of legitimate Vauxhall dealers on eBay and most cases they will clearly display this and you will be covered. However, there are an equal number of sellers who are not Franchised Dealers who claim to offer manufactures warranty where it would not be eligible. In these cases, it would be down to the discretion of the seller and not the manufacturer.
If your unsure whether you are dealing with Franchised dealer, you can check their details using the Vauxhall Dealer Locater:
It's also worth noting that Vauxhall's 12 month warranty of parts can be redeemed at any Vauxhall main dealer providing the the original invoice from a main dealer is presented. For the sake of selling on ebay you will most likely receive an ebay invoice from whoever you buy from as ,administratively, it's a lot simpler to process. If you do have a problem with a part and you've purchased from a main dealer, contact them and they will be able to provide you with an invoice on their headed paper for that part for you to redeem the warranty.
Finally, for small items the above is perhaps not worth worrying to much, but for higher value items it's worth being careful who you buy from. If in doubt, check with the seller first.