There are so many methods of performing the installation you mention.
Here is a link for one brand of pilot light switches by Leviton:
http://www.leviton.com/sections/techsupp/diagrams8.htm
Any switch controlling an outlet would simply feed a light also.
There are switches with a light in the handle that will illuminate only when the switch is ON.
This is the best method, see the switch part # HBL1201PL on the following link:
http://63.90.33.38/wiring/catalogpages/page_C05.pdf
Install your 2 wire cable from the switch location to the overhang, cable is fine, conduit is not needed if the cable will be installed in an attic, I am assuming.
Do you also realize that the deicing heat cable must be protected by a special ground fault device rated for Equipment Protection at 30 MA ( milliamp). The best method is to install a 30 MA GFI circuit breaker in your circuit breaker panel.
In addition to the switch/pilot light, most brands of deicing cables offer a temperature/moisture controller. This would mount at the overhang outlet, and control the heat tape by only turning on the heat tape if the temp is below 32 deg F, and if there is moisture.. No need to have the heat tape on if the temp is above freezing and if there is no moisture.