According to the Disney Insider & Doombuggies.com, it's August 9th:
August 9, 1969 -
Disneyland's Haunted Mansion attraction opens to Park Guests.
And from
Doombuggies.com, History of the Haunted Mansion & An Attraction Unveiled
When the gates finally did open to the public on August 9, 1969, the public response was overwhelming - to the point that just one week after the Mansion opened, Disneyland set an attendance record of 82,516 patrons. The attraction was an instant hit, and remains a Disneyland favorite after more than thirty[-five] years."
But your wishes are still within the birthday week so you're cool

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