So I've come back with a few numbers from myself.

I've seen him spawn anywhere from 30~98 (4 days~) hours from his last kill. I'll go from testimony in here that he can actually spawn twice in a day if need be. Most of my experiences with him have been 60+ hours.

This last one (as of the time of this post) was the 98 hour one. I missed it and most people got gold. AFKed for all of 10 minutes and I blew my chance.

I'm going to say he's just random.

And I hate him and this stupid system. There's no reason to break his spawn apart as long as 4+ days. Keep it every 24~48 hours. If you add in the fact that he can spawn at times when your server just isn't ready for him, it becomes silly for him to take longer than 48 hours.