Random "time on" and trigger event should include seconds. Don't subestimate thieves recording pattern of a target house. Ligth switching on/off always at 00 seconds is very suspicious unless someone with a syncronized clock and a "toc" live in this house.
Another more realistic approach could be you record the pattern of an normal day with you at home and you move switch on/off some random minutes&seconds. Or you record all days patterns and you select a recorded day randomly.