Removing drivers side instrument panel access opening on a 2000 Buick Century

I am fairly certain that the reason my turn signals do not work (intermittently) on my 2000 Buick Century, is that the flasher/relay needs to be replaced. However, I am having a hard time actually finding or getting to it to replace it.
Some sources have said it is located on the inside of the drivers side dash access panel on the very end of the dash that you see when you open the drivers side front door. Your sources tell me that you cannot remove that panel, unlike the similar fuse box cover panel on the passenger side. Now I cannot figure out quite how to get up inside that area of the car to try and get my eyes and hands on the flasher/relay to remove and replace it. What is the EXACT procedure to get access to that area? There is a fibrous carpet colored panel covering that general area. But I can't quite even figure out how to remove that without damaging the retaining plastic things holding it in place. Please give me the best description you can to open that area up and be able to access and change that flasher/relay unit. Thank you

I looked in the engine compartment, which is seems you are saying it is there, but there was nothing remotely resembling this picture in there. So, I have to assume it is on the passenger compartment drivers side of the firewall behind the engine compartment. Which is helpful, but it still brings me back to my original question, which you did not answer. How do I safely remove all the carpet textured and colored panel above the driver's legs without breaking the fasteners, etc. Please give a detailed explanation of that process. I did contribute money for your assistance, and if you would clearly and completely answer my actual question, I would be more than happy to give a much more generous donation the next time I have a question. Please help. In fact, if you can actually assist me in solving my problem of finding and gaining access to this part, I will make another donation right now. Please help.
Thank you,
Tom Wright

Seems like "plastic push pins". How do you remove them without breaking them? Thanks for your help.
Tom

I have one of those! I inherited it from my father in law. Always wondered what it was for! Thank you. I appreciate your help.
Tom