Why is my hold light on?

The "Hold" light on a 2003 Mitsubishi Montero typically indicates an issue with the transmission's hold feature.

So, the first thing to do is check the transmission fluid and if okay I would service the transmission. Here are generic guides to help you step by step with instructions in the diagrams below to show you how on your car:

https://www.2carpros.com/articles/how-to-check-and-add-transmission-fluid

and

https://www.2carpros.com/articles/how-to-service-an-automatic-transmission

Fluid Types
Transmission fluid .................... DIAMOND ATF SP III or Equivalent

Capacities
Automatic Transmission fluid .................... 9.7 L (10.2 quarts)

Check out the images (below). Please upload pictures or videos of the problem so we can see what's going on.