Is it possible to rotate a token rather than a password using AWS Secrets Manager Rotation by Lambda function?

I'm looking at the possibility of using AWS Secrets Manager Rotation by Lambda function to rotate a couple of access tokens for external services. However, reading through https://docs.aws.amazon.com/secretsmanager/latest/userguide/rotate-secrets_lambda.html and the examples provided, it appears that the rotation workflow is only designed to handle passwords, not tokens. That is to say, that the workflow relies on you being able to create the new secret value yourself, and then tell the service being accessed to use that new secret. Which of course, does not cater for access tokens, which you normally rotate by asking the service being accessed for a new token, which it then provides - you normally do not get to create token values yourself. Am I correct? Is AWS Secrets Manager Rotation not usable for rotating tokens that are provided to you by the service being accessed? Because if so, this seems a major gap in functionality.