I’ve tried many options for this, there is no golden answer. It depends on the clients I’m working with at the time. Some clients are going to send you triggering email overnight or early, if so, I’ll leave email off until late morning.
As a travelling house sitter (for over six years now), email for that account is checked several times a day, as early as 6:00am, as it is important to jump in with a response, or the sit goes to someone else. It’s an unusually competitive world, housesitting.
In an ideal world, I would do email once a day, just after lunch. But the world is in constant change, and so am I. Some clients are in Costa Rica, some in Japan, some in New Zealand, some in Europe, so it depends who I need to contact, and how soon I need a response. I work with a World Clock, rather than my local clock.