B1875 means that the turn signal switch is sometimes giving the wrong resistance value. This resistance is read by the instrument cluster. The instrument cluster generates this code.
B1265 is a false code. It is generated by the DATC. Ignore it.
B1262 says there is sometimes a problem with the actuator for the defrost air door. This code comes from the DATC. It's not uncommon at your car's age. If there is no actual problem, then ignore it.
I know you keep wanting to blame the PCM, but why? It has absolutely nothing to do with any of those codes. It is not generating or reporting them. You can unplug the PCM and put it in another room, and your car will still report those same codes (along with a few more that complain that the PCM is no longer talking to the other modules).
Also if I end up having problems down the road from B1262 am I safe to assume the dash will have to be removed for that?
The LS does not have a singular BCM. Instead, it has the FEM, the REM, the DATC, the RCM, the instrument cluster, and so on.
Please understand that the PCM on the LS only runs the engine, the transmission, the throttle, and the emissions stuff. It is not at all involved with the codes you have above.