Can't Figure Out IL Lease Tax Calculations

In preparing for the process of moving into our next leases, I've been going over our past leases to reacquaint myself with all the numbers. Almost all of my calculations work out consistently across all of my past leases, but I can't seem to get a handle on the taxes because, for our current leases, the taxes just don't seem right.
My car : Sale Price ~$24,500, Adj. Cap ~$23,400, Residual ~$12,342, Taxes ~$1195, Mo.Pay. ~$333)
Wife's car : Sale ~$19,700, Adj. Cap ~16,700, Residual ~$9925, Taxes ~$1230, Mo.Pay. ~$249)
So despite having a higher purchase price, a much higher Adj. Cap, and a higher monthly payment, the taxes on my car were $35 less than on my wife's car. That doesn't make sense to me.
A few years ago, Illinois changed from taxing the full purchase price to only taxing the monthly payment and any down payment. We put no money down on either car, so it should have just been the monthly payment. The total sales tax for suburban Cook county is 8.25% + a $15 flat fee, so based on my understanding, the tax on the monthly payments (after excluding the tax amount from the calculations) results in ~$903 for my car and ~$645 for my wife's car.
So what am I missing? Why are the taxes inconsistent, and what's the correct way to consistently calculate the taxes on a vehicle lease?
My car : Sale Price ~$24,500, Adj. Cap ~$23,400, Residual ~$12,342, Taxes ~$1195, Mo.Pay. ~$333)
Wife's car : Sale ~$19,700, Adj. Cap ~16,700, Residual ~$9925, Taxes ~$1230, Mo.Pay. ~$249)
So despite having a higher purchase price, a much higher Adj. Cap, and a higher monthly payment, the taxes on my car were $35 less than on my wife's car. That doesn't make sense to me.
A few years ago, Illinois changed from taxing the full purchase price to only taxing the monthly payment and any down payment. We put no money down on either car, so it should have just been the monthly payment. The total sales tax for suburban Cook county is 8.25% + a $15 flat fee, so based on my understanding, the tax on the monthly payments (after excluding the tax amount from the calculations) results in ~$903 for my car and ~$645 for my wife's car.
So what am I missing? Why are the taxes inconsistent, and what's the correct way to consistently calculate the taxes on a vehicle lease?
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You also have to assess sales tax on the taxable fees - acquisition fee and dealer doc fee, specifically. Those amounts could have been higher for the car and dealer you got the wife's car from, and may account for the difference.
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Ultimately, what I'm looking to find out is, "How *exactly* are the taxes calculated?". There has to be be a clearly defined set of steps for calculating tax on a lease in IL (specifically suburban Cook county). I just want to know what those are. Taxes are the only piece of calculating a lease that I don't have a complete handle on, and I want to be able to accurately calculate taxes on potential future leases so I have all my numbers exactly right before I set foot in a dealership.
+ CAP reductions (this could be customer incentives or cash down payments)
+ taxable fees (anything that isn't a government fee, i.e.: acquisition fee)
= Total taxable amount X tax rate = Tax
Tax is paid upfront. If customer isn't paying it, then it is rolled into the CAP cost, and payment is re-calculated
If taxable fees are rolled into the CAP, then they'll be part of the pre-tax monthly payment, and wouldn't be taxed, again.
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I think part of my problem was that I mistakenly thought that only down payments were taxable when it sounds like any Cap reduction is subject to tax. That makes up a big chunk of the gap, and could explain why the tax on my wife's car was more as her car had $2200 more incentives.
Unfortunately, I still seem to be missing something, though; even adding tax for the Cap reduction, the numbers still aren't lining up.
Car 1
Final Payment (fees included in gross Cap): $333
Pre-tax Payment (i.e. taxes excluded from Cap cost): $298.98
Total of pre-tax payments : $10763.28
Cap reduction: $3022
Calculated taxes (8.25% + $15 flat county fee): $1152.29
Actual taxes paid: $1194.41
Car 2
Final Payment (fees included in gross Cap): $248.48
Pre-tax Payment (i.e. taxes excluded from Cap cost): $211.53
Total of pre-tax payments : $7615.08
Cap reduction: $5200
Calculated taxes (8.25% + $15 flat county fee): $1072.24
Actual taxes paid: $1230.02
What am I doing wrong?
Sorry to keep asking what are probably stupid questions.
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