I think your solution might work. You can also use a bistable relay and a 2-way pushbutton. The relay changes state after giving an impulse to the control port.
https://allegro.pl/oferta/przekaznik-bistabilny-z-przerzutnikiem-sterownie-10559248738?utm_feed=aa34192d-eee2-4419-9a9a-de66b9dfae24&utm_content=supercena&utm_content=ps&utm_source=google&utm_medium=cpc&utm_campaign=_mtrzcj_czesci_czesci-samochodowe_pla_pmax_sc&ev_campaign_id=18003445430&gclid=CjwKCAiAqt-dBhBcEiwATw-ggBHQLrNQ2OSsT0rg5qoqLpAeL1XmCmoZsYT-R1bRNPOFs9MRrSSRmxoCfc8QAvD_BwE