To my mind, the Eotech Integrated Forend Light is the most nearly perfect option ever made. I know of at least one pro that didn't like it because it is apt to get switched off and on again, or into and out of strobe mode, during a stressful situation, but I believe its advantages outweigh that possibility. It's got temporary on, always on, and a strobe mode, plus a lockout switch so it doesn't get turned on by accident in the safe or case. Takes one CR123 battery and is quite bright. It completely replaces the factory grip and takes some getting used to due to the different feel, but it's a great and useful light. Models for 870 or Mossberg are available.
Last I knew, Eotech had discontinued them, but if you can find one...