I had an experience similar to that when I lived in Hawaii except it was roaches..Hawaii's number one pet...lol
We had just moved into an apt. next to the Ala Wai canal and the first night I woke up hearing something rustling, like you said, and when I flipped on the light there were roaches crawling on the walls in the bedroom.  I went right out and spent the night in the car and the next day they brought in an exterminator.   They got rid of everything that day and guaranteed the job for 6 mon. and we never had another problem..
I felt like I was in a horror movie...

 

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[Stuart Chase]