What you are refering to as the fuel pump relay, is called the PGM-FI (programable fuel inj.) relay. I have included a diagram of where it is located.
The light will come on when one of the sensors in the system sends an out of range signal to the computer. If the vehicle is running ok, it is probably emissions related and shouldn't cost too much too repair.
If you take your vehicle to any major auto parts store like Autozone, they will hook up a code reader for FREE and tell you the codes and offer some possible solutions, it may be something you can replace right there and fix it, i have seen bad gas caps cause this many times.
If it's something deeper, post the code numbers here, and we will look them up and point you in the right direction.
If you have further questions on this, please feel free to reply.
Thanks for asking!