Thank you all for your responses.

I've still yet to receive any replies from the seller. Rather than opening a PayPal dispute, for now I've opted to just send the thing back SOD. eBay seems to have accepted the tracking number.

I certainly didn't get offered a "print label" button, though I imagine I might've done if the seller had bothered to open their inbox. I wouldn't know, but that's what eBay's instructions suggested should happen - contact seller for label, print label, post.

I have heard of buyers who didn't receive labels contacted Ebay and they just refunded and told them they no longer needed to return the item.

Ebay priotitize refunding buyers over sellers getting their item back

So you would rather pay for sending back rather than talk to eby on the phone? Not sure why you asked in the first place if you were going to ignore most of the advice anyway!

The gist of the advice I see seemed to be along the lines of "just send the item back" - apologies if that was wrong. I was more concerned about whether that would cause additional problems rather than the $5 it cost me to do so.

Now that you sent the item back,  if the seller is ignoring you, what makes you think you will get a refund? 

I'd like to say "the tracking service", but is there something you know that I don't?

If you just return the item without going through an ebay dispute then the seller can say they have a different address for returns, do it through a dispute and you will be given the address by ebay and there will be no argument as long as you have used registered or SOD service.. 

I've been following eBay's return process, and have used the address given there; I've just been confused by the part where eBay has told me to hurry up and post, despite also telling me to get a label from the seller.

So I've sent the item SOD to the address given to me via eBay's "return details" page (no, I'm not just following some message the seller sent me - I don't have any of those). I'm not sure if simply initiating a return constitutes a "dispute"; the seller a couple of weeks ago who sent me the wrong part told me it was (albeit via Engrish), and knowing eBay, I tend to believe them.

Guess I'll find out the fun way!

Once the item is delivered, eBay will basically see it as a refund becoming due. The initial request has guided steps for the buyer and seller, but it can be escalated if they can't reach a mutual resolution (i.e. either the buyer or the seller can get eBay to "step in and help"), so if it is delivered and a refund isn't issued by the seller (I'd give them one chance, after confirmed delivery, for the seller to respond and/or issue the refund - by which I mean if they don't do either shortly thereafter, I'd message them and request an update etc because delivery has been confirmed), you can escalate it and eBay will make a decision. In general, as long as you've sent it back and delivery can be confirmed via online tracking, a refund will be issued. 

The part arrived Monday, according to AusPost's site - but eBay's tracking didn't pick up on that at the time, despite showing a postage tracking "progress bar" with the AusPost tracking number next to it.

I was intending to message the seller this evening, but it looks like eBay's system finally caught up and marked the item as "delivered". The refund was processed that same minute. So I guess eBay's "post tracking" system just waits for the seller to push a button? Beats me.

In any case, all's well that ends well. Thanks again for the replies!