As you said, if there is a reason then there is no free will (although that needs to be expanded somewhat). If there is no reason then, as I said, it is completely arbitrary. Entirely random. Just as a coin toss.
Free will is actually shorthand for ‘free will decisions’. That’s what we’re actually talking about. Whether we have the ability to make decisions, whoever you class as ‘we’ - the conscious or unconscious aspects of ourselves.
If what has been decided is arbitrary, then ‘you’ haven’t really been involved at all. You cannot reasonably say ‘I decided to have vanilla’ if the choice was made at random. As in a coin toss.
There is no free will associated with random events.