I would confirm I had a fire first before I shut it down for a "Fire Light".
You can confirm it by turning the aircraft to see if you're trailing smoke; there will also be some unusual instrument readings (if you have a fire in the engine bay you'll be getting some weird indications as the wires in the compartement burn through and short out.)
Once the fire is confirmed I would do 1 of 2 things.
1- If I was on approach I would continue to a landing.
2- If I was cruising along and had a fire I would shut it down.
PS: I have had several false engine fire lights in my career but no actual fires.