A couple of ways come to mind;

Template matching https://en.wikipedia.org/wiki/Template_matching

Disregard that the wiki mentions image processing specifically, you can definitely do this with time series data.

grab features of a model wave, then calculate features of subsequent data and match, many ways to do this, you weren’t far off with KNN, maybe try PCA features, wavelets, or FFTs.

Or look at other techniques and think about how to map the featurization of your data to the matching model.