It's random, unfortunately. You need to do the prerequisite event called "A Day in Leon's Life," raise his FP to 10, go on three or more dates, and have lots and lots of patience. You do NOT need the engagement ring or double bed; the guy takes care of these things. You can increase the probability of getting the event by this strategy:
1. Check your calendar to make sure the next day will be clear of birthdays or festivals. Also make sure that Leon isn't waiting to go on a date with you.
2. Check the diary in your room. If there is a Town Event ongoing, resolve it first.
3. Talk to everyone in town to make sure there are no events waiting to be triggered. If one triggers, you need to finish it first.
4. Put Leon in your party, save the game, and go to sleep.
5. If he leaves your party the next day, you got an event with him. Follow him to see where he goes, and if talking to him doesn't get any new dialogue, exit the screen and re-enter from all possible directions or talk to the other townspeople until you see what event triggered.
6. If Leon does not leave your party in step 5, soft reset the game with R + L + Start + Select, load your game, sleep again, and see if he leaves your party. Whether or not the event will activate is random and decided when you wake up at 6 AM. If he does not leave the party, reset and sleep until he does. If you can't get it within a few dozen tries though, it may be best to play through the next day normally and try again some other time.
Best of luck to you!
"Little scratches on people's hearts will be gone if they pat them from behind, but the humans don't know that." -Li'l Cactus White 2: 1636-5705-4662
I actually just accidentally trigger the "A Day in Leon's Life" event while trying to get Arc 3 to start.
The beginning of it, I think it was Volkanon (could be mistaken...) told me that Leon was talking to Vishnal about a book. You head into the butler's quarters part of the castle (from the area south of the castle) and see him talking to Vishnal about some book.
Then I couldn't get anything new to trigger until the next day (no idea why if it is a "day in the life"...) where Leon was talking to Kiel about a book. You enter Airship Way from your farm to get this one to trigger.
Again, couldn't get anything new to trigger. No clue about this book her keeps talking about. So next day comes along. Enter the area outside of the clinic. Dunno if it matters what way you enter but Leon was waiting there. Some spat between Dylas and Doug goes on, and Leon breaks it up.
Again nothing. So next day, I enter the Town Square and Leon is talking to Forte (or was it the other way around) about what he's been teaching to Kiel... they kinda bicker.
Another day goes by. Leon and Lin Fa outside the Inn. Something about delivering a letter to Arthur (even though like, seriously Lin Fa it's like 10 feet away... you can't walk over there yourself?) Follow Leon to Arthur's and they talk about that book that he was searching for. Then, finally the same day another event, outside of the restraunt Kiel and Leon are talking about the book (this whole plot has been about a book, srsly).
And that's the whole event.
Supposedly I had been following him around "all day" despite the fact that it took me several days to complete... (either through lack of time in a day or poor timing... either way!)
Anyways, that's the whole sequence of events. Had I to do it over again I might actually be able to trigger the events in 1 day (maybe...) although doing it day-by-day didn't really matter much seeing as I'm a guy and am not trying to marry Leon at all... still though, might be helpful to someone who IS trying to marry him.