[I'm not sure this is the best place for this kind of question, but I couldn't identify anything better. Please do redirect me if appropriate!]

In the course of engaging in EC261 pedantry, I've discovered that there are not only operating carriers and marketing carriers, but also ticketing carriers.

Operating and marketing carrier I can understand in terms of being "whose actual plane are you flying in" (though I know there are some corner cases with things like "wet/dry/damp lease/ACMI" that I don't really know about) and "whose airline code appears on your ticket" respectively, but what is the ticketing carrier? When will it differ from the marketing carrier, how will I know, and what is the significance if it differs? (My understanding is that for EC261 it's the operating carrier that matters, so marketing v ticketing maybe not relevant, but there might be other impacts?)

The ticketing carrier is the one that issued the ticket and will "pay" on that ticket when redeemed. It is the first three numbers of the ticket, i.e., 001 is AA, 006 is DL, 027 is AS, etc. It will typically be the same as the marketing carrier, but not always, and typically the airline of the most significant segments of your trip, if not issued by the airline directly (i.e., a travel agent).

If issued by an airline, would it ever be different from the marketing carrier?
If issued by a travel agent, when might the ticketing carrier be different from the other two types of carrier?
At what point does the ticketing carrier pay the operating carrier (assuming ticketing carrier same as marketing carrier) or the marketing carrier (and does the marketing carrier in turn pay the operating carrier?)?

Yes, they might be different for many cases. For example, many carriers within an alliance can sell tickets operated by another carrier (the operating carrier). While many of such flights are codeshares (in which case the ticketing carrier would be the same as the marketing carrier), the ticketing carrier can still sell other airlines' ticket in their flight number directly without codeshare. You can easily find e.g. flights in AC flight number on UA website and 016 ticket (especially when a UA flight connects to an AC flight). If that AC flight is operated by a regional carrier e.g. Jazz, then the ticketing carrier would be UA, the marketing carrier would be AC, and the operating carrier would be QK (Jazz), all different.

The same applies to travel agent as well, when there are flight segments by different airlines on the same ticket.

And it doesn't always have to be connecting flights. There was once I bought an Alaska ticket with two connections, and when I checked in, the agent mentioned a risky connection due to weather, so she rebooked me on an AC direct flight. In this case, the ticketing carrier is AS (ticket number 027) and the actual carrier is AC.