This is a recurring issue, every so often when I am driving, my fuel gauge drops to E and the petrol light comes on, after ignoring it (First time this happened, I was quite alarmed, now it is expected.). Does anyone know what is going on here? Is it a defective part, is the car trying to tell me something? I am at a loss here, I am hoping nothing goes wrong wednesday as I have to drive a long way and without money to fix any unforseen issues, it has me a bit concerned. I also hope the two tires in front make the trip as the tread is low and I cannot afford to replace them now, but that is another problem. I just need to know what this gauge drop is and if it is related to the mysterious events that I noticed in the past where the doors refused to stay locked and my radio stayed on with the door ajar and the keys in my pocket.

My dad had the same issue a few years ago with the gas gauge in his GMC Sierra. Ended up being a wiring issue somewhere, I think it was a frayed wire somewhere is the fuel level sensor if I remember correctly.

Gauge cluster stepper motors are defective on S197. OEM parts have been revised to replace original reference. This is a known issue on our cars. I have the same issue on my 2005 GT and sometime, the fuel gauge is indicating full while it's nearly empty or sometimes, after filling the tank, it's indicating half.
You can find repair kits on eBay and How To on Youtube. It's pretty easy to change. I will order a kit soon to change all of them.

Do I need to order replacement parts now, how urgent is it? I already cannot afford 2 tires for the front wheels. How much does this repair cost?

It's not urgent but it's up to you. The only pb, you do not have a clear visibility on your fuel gauge but if you use the daily mileage indicator with the fuel consumption, you know more or less how full is your tank.

I'm inclined to say it's NOT the stepper motors.

I have the stepper motor issue. On cold morning my fuel gauge will read E and won't move until I let the car warm up and then restart it. On other days it will go to 2x as full as it should read and will slowly work its way back down to normal as I cycle the car on/off.

With that said - never once has my low fuel light come on because of this. Fuel light stays off and the "miles to empty" value remains accurate. It's just a malfunction of the motor that controls the fuel gauge, but the rest of the fuel management system works fine.

I'd be more inclined to think OP's problem is either a lose connection (or short) somewhere or a fuel sending unit problem.

I have also heared about deposit issue on the fuel level sensor which can contaminate the mecanism and give a wrong information to the sensor. It happens once to 4 french forumers.

You an clean the connector of your gauge cluster and the connector of the fuel level sensor (right side under rear seats) with electrical connector cleaning spray. This costs nothing (spray + 10 minutes labor)