First, a good quality aircraft soap and scrub with cotton towels by hand....followed by a second wash with standard cleaning brush and hose off all soap residue.
Second, obtain AeroGloss cleaner/wax, or similar product...apply and buff by hand or use buffer...two times if really dirty. This will get the T/B as clean as you're going to get it...if still show signs of exhaust then only a paint job will fix it.
Finish up the first 2 steps with a final coating of Rejex...a teflon based product. Re-apply monthly or as needed to maintain smooth sealed surface on paint...its worth it even on old dirty paint.
Main key is to wash aircraft on regular basis...even by hand with bucket.
As stated above...word of caution on Simple Green, etc type of cleaners that are alkyd based cleaners...they will promote corrosion on aluminum structures. There have been numerous studies on this which resulted in several standards created to classify cleaners as aviation safe. But all is not lost...several mfg's to include Simple Green, I think, have produced a version of their cleaners that meet those standards and plainly state on the exterior of the containers such approval...