Using a neon lamp and resistor across 120 volt contacts with a load resistor in series, the neon will light when the contacts open.
What is the maximum resistance of the load resistor?
Please provide help calculating.
Is there any other discrete device besides a resistor which could be used in series with the contacts and still light the neon when the contacts open?
No relays allowed!

No this is not homework.
It's just a problem I was thinking about going to work yesterday.

 

Use 220kΩ.

A simple google search on neon resistor value finds this:

http://www.intl-lighttech.com/applications/light-sources/neon-lamps

 

In my case the loose wire is often in front or the keyboard.

 

It's relative. Are you behind the wheel or in front of the wheel.