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99% of the time the cause of this is the courtesy switch located inside the hood latch. It starts to corrode over time, which results in an intermittent connection and sets the alarm off by itself. There is a connector near the latch, with a wire harness running into the latch itself.
You can do a couple things here... Either replace the hood latch, or bypass that switch. If you have factory remote start, i would recommend replacing the latch, however bypassing it would confirm that is indeed the cause of your troubles. If bypassed, The alarm won't sound anymore if the hood is opened but Toyota doesn't see that as a problem because in all of their new add-on security systems it just comes with a shorting connector that bypasses where the switch should be anyways. :)
To bypass it, you need to connect the 2 wires together. You can either purchase a scotch lock and crimp it on (and you're done) or you can cut the connector off and manually connect the 2 wires together. If you go the latter route, i would recommend cutting at least a couple inches away from the connector so that you can put it back to the way it is now if you elect to do so some day.
Please try this and let me know if there is anything i can do to help. If you have any additional questions also please let me know.
You got it! please let me know if you have any further questions :)