Our first trip to Iceland was back in 2015 when we did a 3 night stopover. That was fine for a little taste of it, but you are wanting to do more, which is common. I would allow a full day in Reykjavik, the day of arrival assuming you arrive in the morning. Take a SHORT nap in the afternoon and do a northern lights tour that night. This way if the lights do not appear, you have a chance to go again. Then the next day head out on a south coast tour. You don't say when this is, but by October that is winter, so make sure you have good solid winter driving experience, and then know that it may still kick your behind;) Just have plans a, b and c as whether changes so quickly and so drastically. You may want to do a tour for this since they can incorporate ice caves or a glacier hike, which you would need a guide for anyways. I like Troll.is for these excursions.
The problem with Iceland is that there is just so much to see. I head back in September for my 7th visit, and still have so much more to see!
So if you do the south coast and Reykjavik, that is 3 full days. But you may want to add a day trip to Snaefellsness as well. It just depends on how much time you can allow. Also, know that Iceland tends to book out a year in advance, so you are very short notice so lodgings will be a tad harder to find as many will already be booked up. Once you have a rough plan of how many days etc, then post back and we can help you fine tune it.
Oh, the northern lights tour that we have used and was so great was Aurora Experts. I can't speak highly enough about him!
