Having got to the nice position of selling an item/s, it never hurts to follow up with a thank you for the order and payment.
Failing to do so won't lose you the sale of course. But it can leave the buyer wondering whether he should bother to buy your items again.
The guide is to treat your buyer in the same way as you would wish your best ever seller to treat you.
Be sure to leave a feedback, letting your seller know that the item you bought was what you expected. If you fail to do so, your seller might be unwilling to leave you a feedback.
In the end it boils down to common courtesy. As well as showing the ebay community the best arena possible for both Buyers and Sellers.