I dont have to tell u with that reading of 6.5 volts something is wrong.
So it might be time u take it back and have it checked. What they do is charge it up put it on a load tester and see if the bat goes down which u already did.
Not uncommon to get a bad bat.
As long as u checked this on the battery posts u have a bad bat.
Still possible for a bad bat cable/connector.
Yours is doing something i have not seen for example when mine drops below 10 volts the ecu/relays disengage the volts go up an it reengages so u get the click click click instead of the grown u have.
1st optionI would try to exchange the bat for another
2nd u could order the bat that some have had good luck with.
3rd u can go with the top dollar bat with accessorys.
Hth