Besides the useful answers above, search the keyword "aquated electron" or better still "solvated electron". People have been studying theses systems.
https://aip.scitation.org/doi/abs/10.1063/1.455067 For example: Barnett, R. N.; Landman, U.; Nitzan, A. Dynamics and spectra of a solvated electron in water clusters. The Journal of Chemical Physics 1988, 89 (4), 2242–2256 DOI: 10.1063/1.455067.
Of course a free electron cannot exist in water before that will reduce water. It would an interesting thought experiment to irradiate water with gamma rays and simultaneously measure conductivity. You can search along those lines. On the other hand, Grotthus mechanism takes a "proton" movement in solution. For example people still do not fully understand as to why H+ ion has the highest conductivity in aqueous solution. The Grotthus mechanism was proposed a century ago and it resurfaced again.