The major image spell description says:
Similarly, you can cause the illusion to make different sounds at different times, even making it carry on a conversation, for example.
To what lengths can I make the image talk? How many sentences can I make it say or respond with my action?
Best Answer
Ask your DM
Unfortunately, there is very little guidance in the books on how much you can do or can't do with illusions outside of the general guidelines in each spell.
We do know that within Initiative Order, your action and turn take up about 6 seconds. What your action can do with regard to directing the image needs to fit into this timeframe.
With regard to spell description section you quoted above, this is not a live action and response effect. You are using your action to program how the illusion will look and sound. It may not be able to respond in real time depending on your table treats conversations during Initiative Order, but you could have it appear to be in a conversation (most likely with something else in the illusion, but if you're very clever you may be able to make it appear to be responding with generalities. The key difficulty is in that you are using your Action to make it respond. If the other party in communication goes after your turn, you may not be able to respond - but again, that's a table dependent issue.