A.P.
GEICO is usually the lowest insurance company I have found, and that's across many states. Review your policy, make sure you don't have duplicate coverages. For instance, if your deductible is $250 for your collision coverage and you have UMPD, drop the UMPD and keep the UMBI. Or, think about increasing your deductible and putting the deductible money aside in case you need it. If you have an older vehicle, make sure the car is worth more than what you are paying in annual premium for collision coverage. You can look into non-standard carriers like Fred Loya, Safe Auto, and Bristol West, but they usually have higher rates because they insure more "at-risk" drivers.
See if you can make him a weekend-only driver. My mother had GEICO and that's what she did with me until I got married/graduated college. You can also see if you can put him only on one car, but Texas policies usually don't work that way.
Whatever you decide to do, you should put him on your policy. I work for an auto insurance company. Technically, you don't HAVE to put them on the policy, but it will come back to bite you. I am in the claims department and yes, we handle claims where teens who are not a rated driver on the policy get in an accident. But we send a notice to underwriting who contacts your agent that your rate is increasing. So you can run the risk and hope they don't get in an accident. And just an FYI, ANYONE in your household who is a licensed driver and has regular use of your vehicle must be rated on the policy. It can be your child, cousin Susie, Aunt Barbara, Granddad Pete, or your best friend Bob. In the household = on the auto policy! HTH and GL!