Need some help with schematic and (code?) for RX / TX servo controller project

I am trying to assist my son with a science fair project. The fair is based on wireless technology, so my son would like to make a robotic head. The basic design is a gimbal (pan/tilt) with a mannequins head on it. My son, would like to be able to push a bottom (on/off) on the TX box that will light the eyes up in the mannequin, and then at some point when you hit the button again, the light is off. So I am assuming a 3 channel RX/TX?

The "gimbal" will be controlled with a head tracker that we have built, and seems to be working (according to the GUI that came with the open source software) LINK for head tracker: https://www.rcgroups.com/forums/showthread.php?t=1677559

So basically, as you move your head the gimbal should track it. We have been looking around for a simple rx/tx schematic but cannot seem to find anything. We found one, but the "sketch" for the Ardunio would not work, multiple errors.

A few things that are worth mentioning: it is a wireless based science fair, so would like a schematic code, that can avoid interference from other wireless projects, if possible.

If anyone can assist me, I would greatly appreciate it. I don't know where to start, so a schematic, and some code? if necessary/required would be a great starting point. Willing to learn. I greatly appreciate it. Thanks!

based on wireless technology

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Does it have to work by radio frequency? Or can it be by light transmission? Or ultrasonic?

Do you want to make a homebrew radio system? It involves effort and knowledge. As a first project it will be difficult to make it work right. Both transmitter and receive need to be adjusted to the same frequency. Unless you're allowed to use a hobbyist commercial system.

Light/infrared, or ultrasonic are much easier to construct.

Use XBee Transreceivers (2 nos.) One connected to Rx (Robot) and another to Tx (Transmitter / Remote). I can help you if you can use XBee and PIC microcontroller. My Choice of microcontroller is PIC18F26K22. It is a 28 pin microcontroller. I can post mikroC PRO PIC code here.

Edit:

You have to use 2x PIC18LF26K22 and 2x XBee S2 Transreceivers. Some other handful of components are needed.