FOTL at my store has a pretty set schedule 8-4:30.Sometimes, he'll come early to let Inbounds in, but he never closes. As long as fulfillment is properly trained it doesn't really need a TL present at all times. My store doesn't have SFS so that probably makes a difference. But, I've been 100% trusted to run the department before the FOTL comes in or when he's off for the day for a couple of years now. Every TL in the building knows I hate asking for help from other departments and I'll send as many people out as possible. Our SD even defers to me. OPUs are much quieter at night for us, so the Closing TL is adequate to keep an eye on it.
Things don't go as smoothly when both me and the FOTL are off. So, we'll see what happens now that I'm out of the department. But, consider mentoring a TM or two so that they can be you when you aren't there and let other leadership know that those TMs have your trust.