I wouldn't use the standard TLC plate for a mixture as complex as that. Here're two examples for a TLC plate:
1). A pharmaceutical, freshly prepared, and another sample of the same pharmaceutical, extracted from some pills left in a cupboard above the oven for six months. I'd spot them side-by-side on the TLC plate with the same solvent system, and see if they travel the same, without a lumpy shape, or extra spots for the cooked one. And yes, this is a application noted in the US Pharmacopoeia. Notice, I mentioned a pre-purification step for the pills, not a grind some up and smear. And yes, people do do that to their medicine, and yes, pharmaceutical companies do have to test the pills afterward.
2). On one plate, I'd plate out a sample of malic acid, lactic acid and a several samples of wine, from different time points in it's fermentation. As time passes, the wine samples will show less and less of the malic acid spot, and more and more of the lactic acid spot. And yes, some wines do gain a flavor benefit from this type of fermentation.
For your complex petroleum mixture, I would still use chromatography, just not Thin Layer Chromatography, it lacks the resolution of gas chromatography, and the ability to handle large volumes like liquid chromatography.
Something people often fail to realize is that no one gives you a sample and says, "You the chemist, you figure out what it is and how to analyze it." There's generally some idea of what you're looking for.