If you originally sent the item to the address given at checkout, I would advise the buyer that the item has been return by the carrier and request that they advise you on how they wish to proceed. I would then secure the customer's property and await a reply.
If the buyer replies you will need to determine if they are willing to pay to have it reshipped or if they want to cancel the transaction. If they want to cancel, I believe that you can deduct the cost of the original shipping if it was billed as a separate line item, but not if you used free shipping.
If the buyer fails to reply, after keeping the item secure for the amount of time your state deems to be the amount of time unclaimed items are considered abandoned, you can then dispose of it as you see fit. Keeping the money that has been paid as compensation for storing the item.
Of course, if the buyer later makes contact and gives you what you believe is a reasonable explanation as to why it was abandoned, you can refund the buyer as you see fit.
I wouldn't make multiple attempts to contact the buyer. Just one time through eBay messages and maybe one email if you have their email through the order details. Once you've sent those, sit back and wait. The ball is in their court.
"It is an intelligent man that is aware of his own ignorance."
