I spoke to my better half last night as she does work with a fish lab (Yes, they test long term effects of chemicals on fish, the evil woman!!) .
She suggested that even if the dye was permanent, it would disperse over time due to growth. If we are talking 3-4 years she suggested that the “spot” would be large, faded and the edges not clearly defined.
I see her point.
Interestingly (well, to me anyway), the tropical fish trade came under fire for colour injecting Glassfish with dyes to change their colours. The practice is now banned in the UK although the fish are still available freely
The dye lasted about 6 months or until the fish died, which was normally quite quickly. There were even attempts to tattoo fish in the US using lazer dyes. The "scientists" who came up with the idea wrote messages on the sides of fish. Sick!