Actually cache Tap methods.

[reitermarkus]

• Have you followed the guidelines in our Contributing document?
• Have you checked to ensure there aren't other open Pull Requests for the same change?
• Have you added an explanation of what your changes do and why you'd like us to include them?
• Have you written new tests for your changes? Here's an example.
• Have you successfully run brew style with your changes locally?
• Have you successfully run brew typecheck with your changes locally?
• Have you successfully run brew tests with your changes locally?

---

Extracted from #16730 for easier review.

[MikeMcQuaid]

Makes sense to me, thanks!