Ok need a recap on this one. Are these accurate?
The starter is rebuilt
It was spinning strong
Starts well with pull start
Good spark with pull start (another plug in cylinder)
Weak spark with electric start (another plug in cylinder)
Now starter just clicks
If you can reach the power cable post on the starter with a small jumper cable, connect it there, then touch the other end to the postive on the battery. If that spins it strong, it's between the relay/solenoid and the starter. Bad cable, (I know mine was ground down on my pilot by the driven clutch), bad connections, or bad solenoid. You say it's clicking, os it sounds like it's doing it's job...inside connectors may be burnt and not passing full current though.
If it does not start jumping with cable as above, it's in the starter :x or the battery does not have enough juice, but you said it's good.