Insomnia and Being a Call Center Agent

I am a call center agent, which means I have to work weird hours since I am 12 hours away from my customers. I work for a company which supports an antivirus program so basically I'm technical support with occassional moments of purely customer service support.

Lately, my hours have been from 3:30 am to 12:30 noon. I like it for the fact that it's cool and there's virtually no traffic going to the office but I hate it for the going-home part which exactly has the exact opposite weather: too hot and too humid. I hate bringing an umbrella so the jacket which kept me warm inside our freezing office becomes something i put over my head to provide me shade.

Anyway, one MAJOR problem I've been having with this schedule is that I really don't know when the best time to sleep is. The humidity isn't really a problem because there's always the A/C but I don't know, I never get tired enough to sleep in the afternoon and no matter how much I try to force myself to get one, it never happens. That's why I'm afraid that this might be insomnia already. However, around 8 o'clock, I do get sleepy and I don't have any problems going to sleep immediately. Then the issue becomes not being able to sleep enough to endure an 8-hour shift of handling frustrated and irate customers. I've been trying to make my body clock adjust to my schedule but so far, I've had no success in that area. I've also tried a lot of tricks already, like counting sheep and whatever until my head swims with all the numbers it went through.

The point of this post is that I've found that working in the call center industry isn't such a stretch for me, my stats actually show that I am one of the 'performing' agents; that I'm actually very good at it. However, if my body's reaction to the very weird hours continues, which I think would eventually get me sick, then this might mean this work is really not meant for me.