1982 Datsun 710 '82 720 pu won't start

Battery checks out 12 volts, alternator good, just clicks when I try to start it, everything that should beep does, radio works. Sometimes it doesn't even click. Just had a new starter installed a month ago. I have had the battery, alternator checked at 4 different place. All but one says it is good. The mechanic that installed the starter says the battery is bad.