Is there a way for an indefinite technician to get Tricare for his pregnant spouse?

You weren't "labeled" a federal technician, you were hired (you willingly applied) for a job whose benefits are provided for by laws under United States Code; Title 32.

There are certain qualifying life events which allows you to change your coverage. Birth of a child is one. So, this means you should be able to pick a cheaper FEHB plan now - outside of open enrollment season.
Life comes at you fast - which you are learning

For some reason my entire post does not show - earlier I responded from my ipad.

The rest: Your health benefits from the federal government are much better than most offered in private industry. More coverage and cheaper. Adjusting to the cost would be a lot easier if you dropped the entitlement attitude. The only other employer I know of that offers better coverage at lower cost is the United States Post Office. I personally would not trade being a federal technician with FEHB for postal work. The post office is a horrible employer.

Are you a federal or state MILTECH?
If federal, no you are stuck and cannot use Tricare Reserve Select.
If employed by the state, it would depend on state law.

I ran into the same thing when I was a MILTECH; health insurance with nearly the same coverage (give or take some copays) was a full TRIPLE for FEHB than it was under TRS. For no other reason than because some law said so.

Have you gone through the admin?