Selenoid

Hi
Usually when a solenoid is going, everything dims; it might click once. if it was chattering I’d say battery. You could swap solenoid out cheaply enough it’s probably worthwhile.

I would put the battery on a tender/ charger to see if it’s discharging due to a drain somewhere.

Then I would clean every connection with brass brush, emery cloth and vinegar. Uou might just have dirty connections snd maybe a starter needing rebuild

You say the electric start will work fine after you kick start it?
That tells me the battery is discharged prior to kick starting it

Could be last owner ran it with a flat battery and might have cooked the stator. Consider performing test on regulator/rectifier and stator.

You seem to be experiencing a current drain or lack of charge.