"could you show me where eBay (or even the law) specifies how long a buyer has to pay for an item they commit to purchase?"

Unpaid item policy
"When a buyer wins an item or uses Buy It Now to purchase an item, they’re obligated to complete the purchase by sending full payment to the seller.

If a buyer doesn’t pay for an item within 4 days, sellers can open an unpaid item case in the . If the buyer still doesn't pay or reach some other agreement with the seller, eBay may record the unpaid item on the buyer's account." and the seller no longer need provide the item and can relist.

If it was an open ended sale then surely eBay could not terminate the sellers obligation to provide the item to the buyer.  Or are you suggesting that if the buyer has no TAC I can just email after a purchase and say I will pay you in 5 years time.  Doesn't there have to be intent to buy for the contract to valid.  At what point does that end - I really truly intend to pay for it in 5 years time - so stiff wait 5 years for your money?  If that's the case I guess I will take my bat and ball and go home.

PS Since we are being pedantic I never said the buyer did anything illegal I said what they did was wrong not necessarily unlawful, sorry I meant Mean and unthoughtful.