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Is it or is it not illegal to post a 30.07/30.06 sign on a Constable/Tax Office Annex for the County? The JP Office is in a totally separate building with only a connecting sidewalk.

Correct, under penal code 30.06 a political subdivision of the state (county property) is not allowed to restrict license carrying. Unless the location is covered under PC 46.03 restricted access by a license holder. You mention that the JP’s office is in a separate building, you would have to make sure no offices of the JP are located in the building that is posted. If not then they are in violation.

Burnet County Tax Appraisal dist, separate & across the street from the county & district courthouse was once posted, but removed the sign because the sign was a wrongful exclusion of a license holder ....
. HOWEVER next door to Appraisal District is a space that is used for Tax Appraisal HEARINGS and they post it although not a Court, & there's no judge, , under open meetings act I think, although the signs are index card size, if actually posted as "open meetings" at the courthouse across the street the "open meetings" and if a tax appraisal protest qualifies, I didn't check, it could have been be a 46.03 or 46.035 violation (I forget) However, they had no metal detectors, officers nothing but index card signs taped to the glass entrance door.

The Burnet county courthouse annex is still posted, ironically the DPS office was inside there at one time, but moved to another annex which I think is posted in Marble Falls
The license plate appraisal place is inside, but they have drive thru so ltc doesn't need to go inside, I'm unsure about other county secretary etc offices though, If needing to buy a cemetery plot from the city/county secretary on the other side of that metal detector at the annex etc,

This is a Smith County Substation in Precinct 2 on Hwy 155 south. Can you email the Texas AG’s Office? Will that do any good or is it a waste of time?