How to prepare a Gaussian input file for a binary solvent?
I am unaware that this feature exists in Gaussian. It is certainly something that stretches the possibilities of a polarisable continuum model. I am quoting (liberally) from an email to the computational chemistry list (CCL, http://www.ccl.net/), because I found no evidence, that this has changed for Gaussian 16:

Actually, there is no standard approach for solvent mixtures to you use it directly in Gaussian03/09. A good suggestion is to define the solvent parameters as a linear combination of the solvents in the proportions of the mixture.  So for toluene:water in a 4:1 mix use 4/5 of the toluene values plus 1/5 of the water values.
It is recommended to use the SCRF=SMD approach here, but that is not recommended for properties other than solvation free energy. It may be give satisfied results in the case of geometry optimization or energetic properties.  It is especially not recommended for derivative properties, because the cavity for the SCRF=SMD model has a number of continuity issues.  So for the default SCRF=IEFPCM model with the smooth cavity you mainly need the static (or zero-frequency) dielectric constant and the dynamic (or optical) dielectric constant.  You would specify EPS and EPSInf in the additional SCRF input section after the blank line which terminates the structure input.

For example:

{%chk=}
#P {Method, Basis, additional keywords} SCRF=(Solvent=Generic,Read)

{title card}

{charge, multiplicity}
{molecule specification}

EPS=(Add the value of linear combination of both solvents)
EpsInf=(Add the value of linear combination of both solvents)


See the Gaussian Manual for more details.

Another approach is to first do an optimisation and related properties calculation in both pure solvents, and then compare these results. For example the difference in the structures, or spectra.
Since you are using nine parts DMSO and one part water, it might well be that the DMSO calculation is a well enough approximation to the mixture.
Solvent calculations are tricky and often enough unreliable. One should never ever expect a quantitative agreement. It is a qualitative description you should be after.
If you need more accuracy, you have to use an explicit solvent model with MD calculations, or you can look into COSMO-RS.