I was confused because I was calling to make a song request and had no idea that this contest was initiated because they had just played a certain song.

Modern "landlines" when used with DSL or fibre are also no longer "true" landlines, instead the modem/router acts as a SIP client and gives you an FXS port to plug an analog phone into. While it could theoretically emulate this behavior (by keeping the SIP session open for a few more seconds), I don't believe any of them do - in any case it's trivial to test by calling a different phone that you control, hanging up on your "landline" and seeing whether the other phone hangs up immediately (it should) or if the line is held open for some more time.

If this is still a thing (I frankly don't see the purpose of it), it would only apply to real landlines where your phone is directly connected to your phone socket without a modem/router in between.

Someone would call and all the phones would ring (or you might turn off the ringers on some of them so only one main phone actually rings). So someone might pick up the phone in the entrance hall and the caller would ask to speak to Becky, and Becky’s mom would yell up the stairs ‘BECKY PHONE’ and then put the receiver back down while Becky runs into her big sister’s room to grab the upstairs phone, and carry the whole phone, trailing on its wire, into her bedroom, slamming the door on the wire for privacy, before she picks up the receiver to answer.

On the shows they would sometimes hang up the phone, then somebody else picked up a receiver and the call continued?? Phones don't work like that! Go try it on your real phone, and you'll see!

It never occurred to me that US phones worked differently than Aussie phones.

The fact I was so bothered by this probably says an awful lot about what sort of person I was as a child. Its no accident I fell in love with computers.

Editing to add that more detail, since I’m basically contradicting your memory of how it worked:

I’m fairly certain it didn’t work if you dialled out, so you may not have come across the circumstances to test it. Also, the other person would probably also need to be participating in testing it, because otherwise they will hang up as soon as you do.

I’ve just remembered another detail - I think there was something different about the tone you heard. If you received a call, and the other person hung up, you would hear the disconnected beeps. If you made a call, and the recipient hung up, I think you would hear the disconnection, but then just silenced.

By the way - I was also confused by seeing how phones seemed to work in the US - like pushing the hang up sensors (is there a name for these?) once to switch lines for call waiting. I never really connected their strange behaviour with how the phones in Aussie worked.

Actually, is this all related to party lines? I’m fairly sure Aussie had these. NZ did.

Some other comments said there was a timeout after which the call was disconnected if the receiver hangs up.

Well, a few decades ago (80s-90s), at least, landlines sure did work like that in Australia, if you were the one who received the call. I played around with that a lot as a kid. Maybe you just tried it on calls you initiated?

This is dumb though. Just don't put it down until becky picks up.

I could also theorize about the different switching actions going on, where up until the other party picks up there's already only one phone on the line, but that's getting into phone system/phreaking stuff that is way out of my depth.

This is similar to the other answer regarding answering a different phone in the same house, but perhaps more necessary if sharing a line with neighbours. Distinctive ringtones may have made this phone line non-disconnection behaviour unnecessary though.

I’ve never experienced a party line - but they sound ridiculous (and fun).

https://www.evan-doorbell.com/production/group1.htm

The most anecdotal statement ever, but a data point nonetheless.

[0] https://bc.ctvnews.ca/beware-of-the-delayed-disconnect-phone...