I mix my fuel in a 100 gallon transfer tank, usually 40 gallons sometimes 20. I use amsoil interceptor at 40:1 with 100LL. Sometimes with work or bad weather, the tank lasts for a while and may sit for a few weeks. At one point I would run the nozzle back into the fill for a few gallons to make sure the fuel was still mixed, but then figured if there was any sediment on the bottom of the tank that it would then be sucked up by the pump. I store the tank indoors in a heated shop, and it has a particulate filter on it.
My question is, does mixed fuel separate over time?

That's a good question. I've always wondered too but never done anything to verify it one way or the other. I just give whatever can I've mixed a good few shakes before fueling. I have to imagine two-stroke premix oil is formulated to become homogenous.

We always ran ethanol-free 92 octane pump gas and oil injection systems on our two-stroke Rotaxes. Some argue against them for the potential for failure, but it was extremely convenient, and clean. Spilled fuel anywhere just evaporated clean.

I do not care for the spilled fuel leaving the oil residue. But, after seeing what the oil pump gear looks like and the potential for failure, I will mix fuel from here on out. In the first few months of flying with my 582, I was amazed at how little oil it was using with the oil injection system. I had the oil pump arm adjusted about as rich as it would go. I calculated the oil usage per gallon a couple of times, the highest was about 80:1, at the lowest it was about 140:1.
I now mix at 40:1 and, other than oil residue, I have no issues.

Full time 40:1 I think you're gonna gum some stuff up and make more smoke, but it'll be an exciting experiment.

You may have already read this, but if not, it's a good overview: https://www.cps-parts.com/cps/pdf/Part45.pdf

I had not seen that article before, thanks for posting it.

I sent the motor to Rotax Rick about a year ago, it only had 85 hours on it but was 11 years old. He said it looked new, but did find rust on a couple of bearings. While it was there it got overhauled, he put in new ceramic top pistons, double slotted the rods, replaced the main bearings on the ends, decked the cylinders and the head, almost a complete overhaul, but did not split the crank.
He was emphatic about not using the oil injection system. He rattled off several instances of oil pump failures that caused seizures and crashes. He told me of another customer that did as I had done and calculated the oil usage with the injection system. That guy's results were very similar to mine, inconsistent ratios as well as very low usage.
The oil pump gear is plastic, it is driven on a shaft about 1/4" in diameter with a flat driving the gear. While plastics can be some good stuff, I don't like the idea of trusting my life to a plastic gear on a steel shaft with a flat.
With the oil injection system I got splatter of oil all over the tail, I think I actually have less oil on the tail now. I change plugs every 25 hours, and have noticed no greater buildup of carbon on the plugs so far. The exhaust outlet is visually clean with only a film of oil that will stick to a finger. I have now run about 100 gallons of mixed fuel, roughly 32 hours of engine time.
One other reason I did not like the oil injection system is the temperatures I fly in. The oil tank was mounted on the forward top of the motor, it got no heat off the head or cooling system or exhaust. I sometimes fly in temperatures of double digits below zero, with that oil at air temp, it has to be quite thick at 15 below zero. That makes me wonder how hard the pump had to work and how well the oil is delivered in the air stream. Perhaps that is why I got big oil droplets on the tail previously.
I run 100LL because the only local ethanol free gas has had the octane rating dropped to 88, and I wonder how old the gas is. It is also not that much different in price for the 3.5 GPH or less that I use.

Just to touch on oil injection, like all things, when oil injection first came out, there were a few that were against it and remain so, for their personal reasons. That seems to have fallen to the wayside, in the same way that the "new fangled Rotax 912 is too complicated and unreliable" opinion has. Far, far, more 2 strokes have failed due to the issues of improper mixture, etc, than and extremely rare oil pump failure. But, again, there's still a few that are really vocal about the oil injection, just as there are many that believe in it and use it.

There's many benefits to the oil inspection, especially if you are looking for reliability. If you are looking to do any long cross countries, consider the logistics of having to do that with premix. When I flew across the US, it was very easy to arrange for oil deliveries at an FBO about every 400 miles, and them to have it ready, and no muss, no fuss, pour it in the oil tank, no mixing and wondering if it was mixing, etc. Never, never have I had a problem with the oil injection, or had reason to doubt it would not work. The only time I heard of a failure was when someone who thought they were a motorcycle mechanic from their racing days felt they could “tweak” it for better whatever. Leave it alone, follow the Rotax guidelines.

You shouldn't have any oil stains on your rudder. The only time I saw that was when I ran a richer jet, which would explain it. The old injection uses less oil, as it is the ratio will vary, compared to a premix which always has the same amount of oil suspended in the gas, regardless of whether it's idling, or full throttle. I never had an oily film on my muffler, it was either a dark soot, or a whiter soot, depending one whether it was 100LL or auto fuel. Keep in mind I'm not a Rotax expert, but I knew what worked for my 582 because of in depth conversations with experts like Mike Stratman of CPS, who wrote the book on Rotax 2 strokes, and Bevor Borne of Airtech.

Talk to others regarding opinions on oil injection, Bryan Toepfer at CPS, Bevor Borne at Airtech, are just a few. Bryan with CPS I’m sure has some good horror stories. If you can get Bevor away form his Cajun food, he’s an incredible source of info.

https://www.cps-parts.com

https://air-techinc.com

The picture shows how I carried 1/2 gallon of oil on my legs, a simple daypack on the side of my seat. I met some great people on my trips when I would stop at some remote FBO and the guy at the counter would have my 2 stroke oil out and say"I knew this was yours, we never get planes like yours out here looking for oil. " You're in for some great adventures.