I use one light, an XLR-250. I scan with it, then hold it against the forearm to shoot. Takes a little practice to align the light with your point of aim but it's not hard. I am not allowed to attach a light to my guns in my state.
If you can, then mount a XLR-100 on your shotgun, and scan with something else. I'd scan with a XLR-250 handheld. When you spot eyes, drop your handheld and turn on your shotgun light.
A hat mounted light is a popular suggestion here. BUT, keep in mind that you can only turn your head about 150-180 degrees, from one shoulder to the other. It is not uncommon for predators to approach from behind you or from the sides. Using a hat mounted light will seriously decrease your ability to see these tricky animals. Plus your head/neck will get tired of scanning left/right all the time. With a handheld scanning light, you can keep your head relatively motionless and scan with only your hands/wrists while using your eyeballs to scan left/right. SO much easier. And you can actually scan BEHIND you with little movement while turning your head only slightly and using your peripheral vision to see eyes glowing behind you.
Hat mounted lights were designed by and for coon hunters. Period. Coon hunters don't need to scan left/right all night long, they're following dogs and looking into trees. Predator hunters have different needs. If a hat mounted light works for you, great. But they have their drawbacks.