KZ440 Starter - seems like a dead battery but isnt

Hello everyone - recently got a 1980 KZ440 A1 LTD fixer bike.

Starter turns over really slowly, sounding almost as though the battery is really close to dead, although the battery was replaced by PO this year and holds a good charge.

Eventually the bike will fire, but begrudgingly - runs like a top once it does though.

Where do I begin to fix this issue - not worked on starter systems before and eager to dig in.

Check all connections between the battery and starter and the battery to ground Clean and re-tighten them. Also, make sure the battery is the correct size (in amp hours) for your bike. Ed

I've confirmed it's a 12 amp battery, holding really good volts and I've also cleaned and retightened the connections.

No dice - still cranks over really lethargicly, but eventually does fire.

I'm going to try testing the starter relay as outlined in the Clymer - other ideas?

Does it only do this when the engine is cold? Ed

No, but it does start with less cranks when warm, as one might expect, although they are still very slow.

Would it help if I took a video with sound?

1st thing to try
do you know how to use a screwdriver on the starter relay...solenoid

2nd
is the headlight on when the key is on..if so take the two screws that hold the headlight rim on ,off,and unplug the light and set it aside...if the bike fires right up then the battery is the deal...even though the battery checks out...if the light is on before the bike starts....try unplugging it

Thank you so very much for all your help ED

Alright, after digging a bit more, checking all the wires at the battery and the solenoid, I have confirmed that the solenoid clicks nicely, the starter switch works well, and a good battery.

Headlight being removed made no difference, trianglelaguna

Now the solenoid clicks, but the starter motor doesn't engage at all anymore. I have not dug into the motor yet to check it's connection to the solenoid - is that my next step, or is it pretty likely I will need a rebuild kit for the starter motor?