Each panel is made up of multiple layers of acrylic. Partly this is for strength and partly to improve the LED diffusion. If the LEDs are too close to the diffusion segments, you'll see distinct dots. By pushing them just the right distance away they'll still be nice and bright, but look like a single, unified light source.
Refer to the images here for the stacking order.
The bottom layer, cutA, will serve as the back and mounting plane for each panel. It extends higher than the rest and has extra holes for fastening.
cutB is the translucent layer, from it you will cut both the digit diffusion segments and dots as well as a spacer layer to provide offset between the LEDs and the back plane.
cutC is the jig.
cutD is the first of two layers that provide the spacing between the LEDs and the diffusion segements. Its segment cutouts are slightly smaller than the diffusion segments to prevent them from being pushed down toward the LEDs. cutE is the same, just cut from thicker material.
cutF is the top plane layer into which the diffusion segments are inlaid. There are a few variants of these to allow for the different colon and decimal point placements of your timer or clock.
Dry fit your panels together to make sure everything fits, then pull off the top plane and segments so you can use acrylic solvent to permanently bond them.
Apply the acrylic cement with a thin syringe. It will be drawn via capilary forces into the grooves.
Here's how all the layers go together, starting with the top layer (cutF) face down with six screws in it. (Your segments will already be cemented in place, unlike in the photos below, where they are still loose.)