"My mother has a GABA-related neurological condition and has been assured by all her specialists that eating GABA doesn't result in more GABA in your brain. " ---- Did she try it? I would check to make sure it doesn't cause harm or interfere with other things, but "if it can't hurt, but may help" well, who knows.
As walkingman mentioned in post 4, that while ordinary GABA doesn't cross the blood-brain barrier, but you can get some with some transporter which does. "The "Good" GABA is linked to a lipid soluable 'transporter' (usually hydropyridine)"
This may or may not be worth it to people in general, but if your Mother's condition is specifically related to lack of GABA, I personally would consider trying it.
She is on some special prescription medication for her condition, and it seems to help a lot. She's seeing very good doctors who are up on the latest research, so I wouldn't be surprised if they have her try benzodiazepine. She does have some other conditions being treated, so experiments in self-medication wouldn't be wise in her case.