Investigators believe he is armed and dangerous.
Several of Taylor's friends are currently worried about their own safety because Simon has not yet been arrested.
"I just hope we find him," said Christine, one of Taylor's best friends.
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Friends and family are planning to gather Friday at Cleveland Park for a vigil in honor of Taylor.
Meanwhile, federal and local authorities are still on the hunt for Simon.
The 52-year-old left in a dark colored Jeep Cherokee with Texas license plate LYN-0345. Taylor was celebrating her birthday and Christmas with family and friends.
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Simon is well-known in social circles and served on committees for the Houston Livestock Show and Rodeo, according to friends of the victim.
Investigators believe he still has a gun and is considered dangerous. A murder warrant has been issued for him related to the death of Taylor.
Around 15 people were inside a home on Obsidian Drive Tuesday night near the Houston National Golf Club when Simon showed up and forced Taylor outside at gunpoint and shot her to death. Taylor was the only one harmed at the home, according to authorities.
Taylor had gunshot wounds in her head, back, right lower extremity, and right forearm, according to a report from the Harris County Medical Examiner.
Simon also has a mugshot on file with the Harris County Sheriff's Office for a prior offense.
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