bing-wallpaper: update livecheck

[khipp]

Important: Do not tick a checkbox if you haven’t performed its action. Honesty is indispensable for a smooth review process.

In the following questions <cask> is the token of the cask you're submitting.

After making any changes to a cask, existing or new, verify:

• The submission is for a stable version or documented exception.
• brew audit --cask --online <cask> is error-free.
• brew style --fix <cask> reports no offenses.

Additionally, if adding a new cask:

• Named the cask according to the token reference.
• Checked the cask was not already refused (add your cask's name to the end of the search field).
• brew audit --cask --new <cask> worked successfully.
• HOMEBREW_NO_INSTALL_FROM_API=1 brew install --cask <cask> worked successfully.
• brew uninstall --cask <cask> worked successfully.

---

Related to #171006.

[samford]

This livecheck approach looks fine to me. Outside of the comment below, this looks reasonable to me, provided the cask maintainers don't have any issues.