Okay, it's still easy. You put cleats, say of 1X2, about 12" long near the top and the bottom of one of the two panels. Half of the cleat is screwed to one panel's front surface, ideally countersunk, and the other half will cover the same distance and location on the adjoining panel when you get them tight up against each other. You'll drive small screws just deep enough to embed into the front surface of the second panel and snug it up gently, also countersunk. The cleat is rigid and will bring the two panels flush up to each other.
You can paint over the four screws, or cover them with plaster/drywall mud, and paint them when they've been sanded flush. Locate the screw heads later with a magnet, bare them with a knife tip, remove them, separate the modules.