Resolve an issue with automatic flag for timezone (uplift to 1.71.x)

[brave-builds]

Uplift of #26210
Resolves brave/brave-browser#41869

Pre-approval checklist:

• You have tested your change on Nightly.
• This contains text which needs to be translated.
  • There are more than 7 days before the release.
  • I've notified folks in #l10n on Slack that translations are needed.
• The PR milestones match the branch they are landing to.

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Post-merge checklist:

• The associated issue milestone is set to the smallest version that the changes is landed on.

[kjozwiak]

As per discussion with @deeppandya., we'll get the above fixed via 1.72.x. I'm running into issues where I can't get Denver to be selected. @Uni-verse is also running into an issue where Denver isn't being selected once you've re-enabled Automatic. We'll investigate/get the above fixed for 1.72.x.