Since you mentioned tail-ing, I expect that you are comfortable working with the terminal using the CLI tools.
You can install awslogslocally and use it for tailCloudwatch.
eg
$ awslogs get /aws/lambda/my-api-lambda ALL --watch --profile production
Besides the fact that I no longer need to update anything (for what tail), I also like that you do not need to worry about switching between different LogGroups (unlike the CloudWatch console).