How do I show squiggle using a classifier?

I've already implemented an error classification of my own with its own formatting but I'd prefer to actually use standard error conventions. I tried using the "syntax error" classification (as below) instead of my own error classification but there weren't any changes to the text. I've seen documentation indicating that ErrorTag will provide squiggle text but don't know how to tie that in with a classifier (and have been avoiding making a tagger in addition to the classifier.)

errorClassification = registry.GetClassificationType("syntax error");

Is there a way to get a classification to format showing a squiggle?

As an aside, is there something similar to PredefinedClassificationTypeNames that I could use instead of the literal text of "syntax error"?

Thanks!

- Reese