Southern California is not (yet) the old Ottoman Empire where people lived in seeming shacks with opulent interiors to keep the Sultan's tax farmers from noticing and then squeezing them. There's still an if-you've-got-it-flaunt-it attitude that's especially visible in car purchases. Thus, the most straightforward way to tax gray market income would be through a luxury tax on car purchases. For example, besides the existing taxes, you could establish a simple incremental luxury sales tax on new and used car purchases that would be zero percent up through $10,000, then add 1 percentage point for each $10,000 of sales price over that.
Thus, a $20,000 car (e.g., a nice, big, new Ford Fusion or Hyundai Sonata, 4 cylinder, automatic transmission, power everything), would cost an extra $100 in luxury tax.
Price Tax $30,000 - $300 $40,000 - $700 $50,000 - $1200 $60,000 - $1800 $70,000 - $2,500 $80,000 - $3,300 $90,000 - $4,200 $100,000 - $5,200
Of course, cheating on this anti-cheating measure would happen — dealerships would make kickback arrangements with seemingly 3rd party shops to add $4,000 wheels, and the like. But, this seems like a pretty reasonable way to catch a little of the tax evasion that is going on at low cost to the honest and thrifty.