There are a few different ways you can configure a built-in wall aquarium. For clarity purposes I will refer to the 2 sides of the wall as side A and side B. Let start with the best. The ultimate in-wall aquarium will have side A and side B finished and trimmed out. This tank sits flush on both sides of the wall so anyway you look at it, it’s a beautiful clean sharp feature of the house. No wires can be seen and if you look through the tank you will see fish and another room. For installs where the aquarium is wider than the wall you can have one or both sides overhanging. This is not a problem as long as the tank is completely supported underneath with 1 1/2″ of plywood or solid wood screwed into the wall framing. The tank should be boxed in with trim to finished the look.
If side B is a closet or basement or you just don’t want to see through the tank only side A needs to be finished. If possible the tank should be accessed from side B. It will be easier for maintenance than one that is completely sealed in. A backdrop will block anybody from seeing through the tank.
When you look into a built in aquarium you will not be able to see any wires or wood inside the wall. The ends inside the wall will reflect like a mirror.