Is there a way to remotely operate the push-button light brick?
Yes, the easiest way would be to get the following: a powerfunctions remote control, battery box, moter, ir reciever,   and z-motor. The total cost is $36 and you can get all this on LEGO.com except for the z-motor, that part you have to get in a LEGO set as the following: 8052. 8053, 8110, and the LEGO Technic yellow actuator which I can't find the set number of right now. get a 1x4 axle (usually black) put it at the far end of the z-motor and into the light brick. Get another 1x4 axle and put in  the other end of the z-motor and into the regular motor, hook the regular  motor into the receiver, and the receiver into the battery box. Make sure the remote control and the receiver are in channel 1. Make sure the green light is on, on the battery box. The battery box could stay on for about a week without needing new batteries. flick both of the levers on the remote and the  light should turn on. You could also get the rechargeable battery box where it plugs into an outlet and never needs batteries. You could run 32 lights on 1 remote.