As Nilesh suggested, there are commercial gas sensors which can be used. I had to detect H2 so used a commercial gas sensor, and did the electrolysis inside a sealed desiccator filled with nitrogen in the below paper; however, it took a lot of effort to make it quantitative. https://www.researchgate.net/publication/210186429_Clean_efficient_electrolysis_of_formic_acid_via_formation_of_eutectic_ionic_mixtures_with_ammonium_formate
Article Clean, efficient electrolysis of formic acid via formation o...
If you are sure that in your reaction, there isn't other gas evolution, you can use the simple volumetric method. You can use an inverted water-filled burette in a water-filled vessel, and you can monitor the evolution of H2 in the time
You may find more details regarding the volumetric method proposed above in "The Handbook of Homogeneous Hydrogenation" edited by Johannes G de Vries and Cornelis J. Elsevier (published by Wiley-VCH), in particular in the chapter "Kinetics of Homogeneous Hydrogenations: Measurement and Interpretation" (pages 257–293) by Hans-Joachim Drexler, Angelika Preetz, Thomas Schmidt and Detlef Heller.
To monitor the evolution of H2 from a reaction if gas chromatography technique is not available by collecting gas by downward displacement of water in a cylinder kept in an inverted position like Eudiometer tube..
I agree with the researchers who answered yes, it is possible to use a graduated cylinder that contains water, because the volume of water displaced is the percentage of hydrogen.