I think it's fine to send the invoice at this juncture, they could have forgotten or not realised they won.
You could try adding a cheery note saying "Hi, congratulations on winning the auction, I'm happy to get the courier arranged ASAP once I've received payment, let me know if you have any questions about that."
Did you invoice them after the auction ended - if so my advice would be that as soon as 48 hours has passed open an unpaid item case.
When I first began to sell I was far too soft and I would wait a week or more after I'd sent the invoice before I did anything. Nowadays I don't hesitate to act. 5 times out of 10 opening a case has the desired effect and the buyer pays up. If they haven't paid after 4 days from when the case was opened I close the case which means I get my fees refunded and supposedly the non payer gets a strike against them. To my way of thinking this isn't sufficient punishment for a buyer that doesn't pay and if I had my way I'd allow sellers to make mention of non payment or very slow payment in their feedback, but of course this is against eBay rules.
Being someone who would no more think of bidding on something and then not paying I could not believe that there are people who would do this, but there most definitely are. IMHO two days is long enough to wait before you take action. Even then you have to wait another 4 days before you can close the case.
Old hander here at Ebay I have found that a cheerful, "hi, thanks for your purchase, I am ready to send it to you once you have paid, kind regards" etc gives them a bit of a nudge (guilt trip) without being in their faces. Sending an invoice/unpaids asap etc without a cheerful message first puts peoples backs up.... there's a hard way and a soft way, choose the soft way first (then sock it to them )
Hardened seller here. I leave upto a week. So many buyers these days do not pay promptly that it's not worth a second thought.
After a week, I send a cheery message as Oldmittens does and ask them to let me know if they've changed their minds. Most people get back to me then, apologise and pay.
A significant minority just ignore any correspondence and don't pay and I open a case against them. They get a strike (presumably) but seeing as some buyers seem to do this repeatedly, I'm fairly sure that EBay don't give a fuck.
24 hours is way too soon to get huffy with your buyer. You risk getting their back up.
I completely agree with you Lepaskilf. You used to have to wait 4 days to open an unpaid case, luckily eBay recently changed that to 2 days as sellers got sick of waiting. I think 6 days overall is plenty of time to pay. A reminder of an unpaid case being opened is plenty. And if a buyer is never going to pay surely you are better finding out after 6 days, sending a 'cheery' message after a whole week won't make any difference to a non payer. They will just ignore.
Oh and make sure you add them to your blocked bidder list.
I sold something recently and like you was getting frustrated because the buyer had taken longer than expected to pay (2 days). Then I got a lovely apologetic email explaining that she'd gone into labour and had her baby. Since you're selling a pram do you think there's a possibility something similar has happened here?