Arduino project help: light up a big dome pushbutton

Projects General Guidance
1

Need some help as I am new to Arduino...

I have a requirement where I have to light up a Big Pushbutton switch like this: (Big Dome Pushbutton - Red - COM-09181 - SparkFun Electronics) from a location about 5-8 feet. I might add more such pushbutton switch and want to turn them on by pushing a button located 5-8 feet away. I want to make it work similar to a restaurants buzzer sort of. So a user sitting at front desk has four button in front of him ( Red, blue, yellow, green). He then press one of this button in front of him, then one of the big push button, located at about 5-8 feet, would light up. At one time only one such big button need to light up. Please help if you can.

Thanks

2

Turning on a BigPushButton is easy, but when should it go off again?

3

It will go off manually when a user press some sort of thing on the button itself. The idea is just like restaurant pager which goes off when you hand it back at the pager desk. I am confused on how to turn it on without any sort of wired connection.
Thanks