I can't remember if I saw it in a cartoon, a documentary, or both, but the notion is that the clients of cleaner fish wait in line to be cleaned. "Clients" means the fish (or other aquatic animals) who are cleaned by cleaner fish.
I tried to find a study whose sole purpose is to confirm that client fish wait their turn to be cleaned by cleaner fish, but I only found articles that seem to refer to this while studying other cleaner fish behaviour.
Statements I came across that support the notion:
Most photographs of fish in coral reef are at cleaner stations because the fish are waiting there which allows photographers time to photograph.
Cleaner fish "have a positive impact on local reef fish diversity", which could imply many different fish come and may not attack each other to benefit from the cleaner fish. This one's more of a stretch.
"Others wait no longer than 30 seconds before searching for cleaners elsewhere." The source is German, so I can't go deeper.
Do fish wait in line to be cleaned by cleaner fish?
Side question: Is this an example of reciprocal altruism?