Ok. The rental unit is empty. Have you been renting out it, or has it never yet been put into service as a rental? Why is it empty now?
If I assume that the rental qualifies as an active rental and that the work you need done is just repair work rather than improvements to the property, then it works out like this.
Let's suppose you hire the S-corporation to do the repair work for you. The repair work takes 50 hours to do and you bill the labor at $50/hour, so that's a total of $2,500 for the labor. The S-corporation pays you $35/hour for the 50 hours of work, so you get paid $1,750 for that.
That $1,750 of wage income is taxable income to you. In addition to that, you'll have 15.3% of that amount to pay for FICA (Social Security and Medicare) taxes, half paid by you via a payroll deduction and half paid the corporation itself. So the total FICA tax is $267.75, your half of which is $138.88 and the employer's half is $138.87.
The corporation has $2,500 in income for your labor. It gets to deduct from that the $1,750 it paid you for the work, and the half of the FICA tax it paid for you, for a total deduction of $1,883.87. That leaves a profit of $616.13 on the labor for the job. That profit then flows up to you to be reported on Schedule E of your return. It is not just the amount of profit you distribute that is included in your income; the entire profit of the S-corporation is included in your income.
Now, I assume the duplex is simply owned by you personally or through a single member LLC that is disregarded for federal tax purposes. the money you paid for repairs would be a deduction for the rental activity, assuming it is an active rental. (If the work were improvements to the duplex, it would not be a deduction but rather an addition to basis.) So that's a deduction of $2,500.
So what do you have at the end of this. You paid $2,500 to the S-corporation for the labor for the repair, which you deduct. You ended up with income of $1,750 in wages plus $616.13 in profit from the S-corporation, for total income to you on your personal return of $2,366.13 on your return. So the net difference is a reduction in taxable income of $133.87. If you were in the 24% tax bracket that means your total income tax savings from using the S-corporation is $32.13. You'd also save $6.20 in Colorado income tax. But you also ended up paying $267.75 in FICA taxes for your labor. So in the end, you saved a total in income tax of $38.33 but paid out $267.75 in FICA taxes for it. Ultimately it's costing you tax in this example of $229.42 to do it this way
Now let's look at the alternative way you could do the repairs. Again, assuming you own the duplex yourself or through a single member LLC, you could just do the work as the landlord and not go through the LLC. Your labor in that case results in no taxable income to you nor any deduction for you. As a result, there is also no FICA tax for you to pay for your labor. There is simply no tax impact for your labor. So you'd be better off doing it this way because you don't have that FICA hit you take running the work through the S-corporation.
Note that if there were no FICA taxes the result would have been the same either way — no ultimate tax impact. So you'd still not save any tax running it through the S-corporation. But because you do have pay FICA taxes on your wages, it ends up being worse for you to use the S-corporation.