There is a distinction between fluorescent coolant dye and UV (Ultra Violet light) flourescent coolant dye. Years ago you could just buy a coloured dye and add this to the coolant. It was usually green stuff, sometimes yellow, and could easily be seen, even in difficult places with an ordinary, yes ordinary, torch, if necessary. The UV dyes are not really necessary for coolant leaks, although they might make a leak easier to see....BUT.....you will need a UV torch to see a leak to best effect. UV dyes are often used for air- con leaks, although as kits or bottles they can be expensive.
Think about it for a moment. Most leaking fluids can be easily found if the leak is from a hose which might be split or life expended and due to be changed..........leaking fluid is fairly easy to detected, sometimes external to the vehicle, perhaps on the floor. Sometimes the air-con might leak into the vehicle, as might engine coolant from a heater hose.......HOWEVER......leaks internal to a vehicles passenger compartment are pretty rare. Leaks are most often found under the bonnet / hood.
Where fluorescent dyes come into their own is in detecting pin-prick holes in a radiator matrix, (often difficult to spot), or at, say, a radiator cap seal.
Any trace colourant in the water / coolant of an engine coolant system will usually suffice. I have previously used a food colourant liquid as a dye and it has worked well. All that is required afterwards, and presumably once the leak has been detected, is to drain and flush, then after any necessary repairs all that is required is to refill the system with coolant.
You will not cause any damage to an engine, or its seals or gaskets with a simple coloured trace element in a cooling system to detect a leak.
Washing up liquid can be used, (remember how we always use it in water to detect a leak in a tyre inner tube, be it bicycle or car). All you do is to watch for the bubbles. If you do use washing up liquid you have to remember that it is VERY concentrated in the form in which we usually buy it........so you will need VERY LITTLE of it. You will need to flush it out with cold water afterwards. If you use too much of it you might need to flush the coolant system a couple of times.
Experiment with washing-up liquid in a washing up bowl at the kitchen sink and you will see how little of it is necessary to create enough bubbles. The more you use, as a squirt, say when washing-up crockery, the more bubbles you have.........and the more you will use.......The more you use the more the manufacturers will love you as they can sell you more bottles. I digress slightly here, but you get the point.
Washing-up liquid reduces the surface tension of the water, when washing-up, and so helps to cut through grease. If used in a coolant system to detect leaks, the surface tension component is not important since you will only be looking for the bubbles.