The high beam lights on my 2002 saturn sl will not shut off unless i pull the fuses. The light stays on even when car is off. With the fuses pulled out the high beam indicator on the dash continues to flash.

It's the turn signal switch that is faulty.

I would test the relay to make sure it is still good and everything there is working like it is supposed to. I would also look at the switch and make sure noting came unplugged and it is still in good working order sometimes new parts are still bad.

Faulty switch.

Replace the switch that controls the high and low beam

the head light assemblies hold high and low beam bulb units. they come out by turning 30 degrees and a gentle pull. do not touch the glass part on the new ones and make sure you are putting the bulbs in the correct sockets as the sockets for both bulbs are the same, just different connectors.

it sounds like a bad light switch

you have hot grond

pull the bulb out and look for burnt spots on the connector. if it's burnt or corroded you can get a replacement at a good auto parts store

You probably have a faulty sentinel switch. It's supposed to shut off, has a bult in elctronic timer. Does it even have the sentinel switch?

have you actually checked the bulbs wit a vom and if not, do that first, second check power to high beams, thord check high beam relay and fuse, fourth check switch. Complete directions or available online if you need a link. I hope this info helps you solve your problem, Merry Christmas!