What is the purpose of the Dash 8’s “TOUCHED RUNWAY” warning light?
The light is a tail-strike indicator.


  Touched Runway system 
  
  The  Touched  Runway  system  provides  a  warning  light  in  the  flight  compartment.  It  illuminates when the aft fuselage makes hard contact with the runway on take off or landing. The system consists of a frangible1  switch located at the bottom of the aft fuselage, activating the warning light. The system is powered from the 28 Volt DC right main bus. Once activated, the frangible switch can not be reset but must be replaced by maintenance personnel. Source: Smart Cockpit.


1 frangible
/ˈfran(d)ʒɪb(ə)l/,
adjective


able to be broken into fragments; brittle or fragile.
"the frangible skull of an infant"
denoting ammunition designed to disintegrate into very small particles on impact.
    "frangible bullets"




Figure 1. Source: ATSB.au.



Figure 2. Source: ATSB.au.



Links:


Tail strikes during landing involving Bombardier DHC 8 402, VH-QOT and VH-QOS.
AAIB Bulletin: 10/2017 G-ECOJ EW/G2017/01/03.