The problem is that I haven't used a LA since 1986 so I am a little out of date. Narrowing down the options to pg 47-50 helps a lot. The table on pg46 only has one dot for 1650 series.
The information that's relevant to you is what they call 40-pin connectors. 90-pin connectors was something that came in the early 2000's for their high-end logic analyzers. Also anything about Mictor and other PCB connectors is irrelevant for you, because those are only helpful if you're designing your own boards with them in it.
I found a HP reference here https://edadocs.software.keysight.com/kkbopen/what-digital-probe-cables-and-accessories-are-available-for-keysight-mixed-signal-oscilloscopes-msos-589743268.html.
It says the 01650-61607 cable was useful but I am not certain if these are all compatible with my HP 54546D scope.
Search for pictures of either the cable or the end that takes the cable (e.g. HP 1650A/B, 1651A/B, 1652A/B, 1653A/B in the case of 01650-61607, and HP 16510A in the case of the 16510-* cables). It should only have one pod connection (so 16-pins), not two pods as many later cables. And the logic analyzer side should look like an IDE cable (40 pins 0.1"). The pod side always looks like that. If 16510-61602 is compatible, then probably so is 16510-61601 (one is shielded and the other is not shielded). From the pictures it looks like 01650-61607 is shorter, and the 16510 cables seem to have an odd right-angle 40 pin connector, so I'd try to find 01650-61607 if possible.
I did try plugging in a standard hard drive cable but the connectors have one pin plugged, so that doesn't work. I found a seller nbhightech on e-bay that advertises "Agilent HP 10089A Logic Probe with Flying Leads for 54620C". Sort of a semi DIY solution. I assume the little pcbs have the passive terminator components.
Not all IDE cables have that pin plugged, and you can remove the pin with a sharp objet. It's generally just press fit. But you might miss on a signal or ground connection, and signal integrity won't be the best without twisting and especially without resistive conductors.
I tried that search and got a lot of hits on pods but no pouches. I am unsure whether these pods plug straight into the scope, or if there should be a cable between the scope and the pod. Many listings include references to K,M&N clocks. I don't know if that is something I need to worry about.
No, you need a cable between the scope and the pod. Ignore the stuff about different clocks, that's only stickers so on logic analyzers with multiple pods you know which pod corresponds to which clock.
As for one with all accessories, see for example
this one. Not sure if that's the cheapest price. It might also help to search for HP/Agilent E5383A or 01650-61608. Something like
This listing (I have no relation or experience with this seller) might be interesting, since it appears to come with a cable that looks like it might work, although I prefer the latter flat clips to these round clips. You'll have to search for Australian listings on your own, but this might give you an indication on what to search for. Sellers may not always use the correct part numbers since I don't think they are printed on the cables. At least not very obviously. So it might pay to scroll through a bunch of "hp logic analyzer cable" listings.