there is a pressure switch inline with the LP fuel lines, check it and make sure it is not stuck closed.
use ohm meter and read across it, with pressure on it the circuit should be open so the light will not illuminate, then shut off the valve on the LP tank and run engine till it runs out of fuel and engine shuts down, at some point just before that the pressure should drop enough in the lines to close the switch and turn on the light.

if it does not do this then replace the switch