My understanding of the shooting only lasting for 11min and the SWAT team not breaching the door for around an hour was that SP stopped shooting when the lone security guard randomly walked by his room and he shot him in the leg through the door. I believe they think he spent the next little bit figuring out if he could still try to escape, but when he saw SWAT approach, he then shot himself.
Security guard alerted LE to shooters location via some sort of communication device but I think SWAT still had to clear the hotel room by room.
I may be wrong on this but I know I read this somewhere or heard in an interview. I'll try to find link.
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As far as I can tell, they haven't heard when exactly he shot himself.