That link is for time dependent DFT (TD-DFT), which can work if you have already calibrated the functional against robust many-body approaches and the states are largely single reference in nature. If you have states that are more complicated (highly-correlated, doubly excited, etc.) TD-DFT will not just fail to accurately describe them but will miss them entirely as well as mix other states, complicating the interpretation of any spectra.
While Gaussian has EOMCCSD this is not recommended as their CC codes are extremely slow, even those that can be run in parallel, and while EOMCCSD can capture some of these more complicated electronic states, it cannot accurately describe them as higher-order excitations are required for this. If you are looking for Rydberg states you will run into issues of basis set size as well, which can greatly increase the computational time when using a many-body based approach.
Gaussian does have available SAC-CI which is a robust and accurate single-reference many-body approach that includes higher than double excitations. For examples and keywords, see the following:
If you want to locate the lowest two singlet excited states, you could use a route like the following:
# SAC-CI=(Singlet=(NState=8))/6-31G(d) NoSymm …
This will search for 8 singlet states, ignoring symmetry. The two lowest excited states will probably be among those found by the calculation.
Alternatively, you could use the following route:
# SAC-CI=(Singlet=(NState=4))/6-31G(d) …
This calculation will locate the lowest four singlet excited states for each irreducible representation.
To specify the desired number of singlet excited states for each irreducible representation for a molecule with C2v symmetry, use a route like this one:
If you're not tied to Gaussian, there are other open-source and/or free programs available that offer robust approaches as well as sometimes being faster than Gaussian, depending on what you need.