Our old boy likes to drink from outside water,(rains a lot here in the North😁) he used to use an old cleaned out takeaway plastic container, but then i bought a washing up bowl that wasnt deep enough for sink,so i put it outside,& by chance he spotted the rainwater had gathered in it,so he makes a point of drinking from that everyday.We have got him an inside water bottle,but since moving i dont think he likes the taste of the tap water.The bottle is similiar to the ones in offices etc but smaller (you know the upside down big water bottles?) But it lets down into a type of dish/holder,so its constantly filling as he laps the water,But as i said he wont use it as much with new water supply(i think its very chlorine-tasting here)He did love it at old house.They've probably got them on amazon or somewhere.Trouble with leaving taps running is it can be costly i imagine if you have a water meter,or wasteful of water resources anyway if you havent.Our cat has never liked it from tap anyway.Have you tried your cat with the specialised cat milk,or the Hydralife cat drinks or cat soups that are available now? Hydralife in particular is very good to help quench their thirst, i got my cat some in hot weather just so he was drinking enough when indoors.