1990 Toyota Camry dashboard brake and charge lights on

I have a 1990 Toyota Camry, 225,000 miles, manual transmission, 2.0L where the dashboard brake and charge lights are on. I have taken off the alternator and taken it to two automotive stores, both tested it in an table top alternator testor and it passed (Amp/Diode Trio, Regulator, Rectifier says all passed). Drove the Camry to the retail store where I bought the battery and to a repair shop for a free check, one says the battery (3 1/2 years old) is fine and the other says there is a problem with the charging system. I switched battery to another car and that started okay, and appears charging okay. On the Camry, battery reads 12.7 V when not stared, and 12.6V when car started, both brake and charge lights on. When battery is freshly recharged, both light go off when car is started and hand brake released, but within 30 minutes or so of the car running, both lights come on. A few times, the car seems to have died when slowing / low rpm, but then jerks and revives, this doesn't happen all the time. A few times, after driving, I turn off the car and try to restart, but the car will not restart.

Could the alternator be bad even if the off-car tests passed? How could I check that with a volt meter? Voltage on ground terminal (F) and positive (B) on alternator is less than voltage between + and - on battery when car running. [Battery drain, thus the recharging of battery]. Are there any cables other than those connected to the alternator that could have broke/loosen which could cause the battery not to charge AND low voltage at alternator?