My 97 Oldsmobile Lss has been running hot. Fuel pump stays on. Is this normal

Hello, When does the fuel pump stay on? can you always hear it running? It should not be. It should only run constantly when the key is turned. You have a leak somewhere, get a UV dye kit for engine cooling systems, and a UV flashlight. That will show you where the leak is by glowing. If the overflow stays full, but the radiator is not, test the radiator cap, and make sure there are no clogs in the line from the radiator cap to the overflow. Let me know what you find.