i have ran into this problem before with the genie charger
in the genie charger manual it does not list a 8 blink code, it only goes up to a 4 blink code as you describe.
But the problem is an internal fault in the charger start circuit. As you said it goes through its self check and then the relay clicking is when it goes into charge mode. Apparently there is a fault with the transformer or it could even be detecting a battery issue. If you have checked the batteries and ruled out those then the only avenue you have is to replace the charger itself. Thats what i wound up doing and it fixed the problem.
I never did find out what the 8 blinks meant though.

i did check on genie's site though and there is no genie model like you described "HB600"? and the part number came up bad too. Are you sure on this information about the machine? This is the information off of the dataplate? NOT the decals on the machine but the dataplate information.
Model Number?
Serial number?
mfg date?
revision code if there is one?

???