It was clamped together before it came apart, so it really needs to be clamped together again. Just remember that the centre block isn't that wide (you may be able to use a torch and a small inspection mirror to check through the f-holes), so keep the clamp near the edge of the cavity. If you move the clamp too far away from the edge and the wood will pivot on the edge of the block and the gap at the cavity edge will open up even more. Definitely protect the top's finish with some soft wood blocks and some cloth first.

It's probably the right time to check the pickup cavities for fit with the pickups before you start with any finish. I fettled an ES-1 (for someone else) that had Tonerider AC-4s, and the end tabs on the pickups fouled the sides of the cut-out, so they needed to be widened.