There was some discussion about this very circuit recently at https://pinside.com/pinball/forum/topic/playball-doesn-t-wait-for-flipper-to-shoot-ball-except-on-1st-ball. That topic might provide some insight into how it should work.

If your kicker keeps kicking it's likely because the Score Motor runs longer than it should, which repeatedly closes the Score Motor 2C switch that fires the Ball Return:
Playball Ball return (resized).jpg
The other normally open switch in the Ball Return circuit is on the O/Ball Return Control relay which is activated when the ball drains and remains active until points are scored, so that switch is probably closed.

To figure out why he Score Motor keeps turning you need to check all the relays that can close switches that can start the Score Motor (W, E, P, S, etc.). It could be that either one of those switches doesn't open reliably, or that the relay that closes the switch is active longer than it should be, which keeps the Score Motor running.

/Mark

These spring loaded pins are sometimes called snow shoes. They may be connected by the solid wire soldered between their sleeves but a flexible jumper soldered between these two pins would be more reliable. Fine solder wick works in a pinch. These two are likely represented by the symbol in the red box:
Playball Ball Count 2 (resized).jpg
which is used after the last ball drains to award a replay through the match circuit.

The Vari Target won't reach the Home Run when hit by the ball, or won't reach even if you push it back with your finger? Either way, if it's sticky you should clean both the contact board and the wipers. You should be able to push it back with your finger and have it lock in any position, and also have it completely reset if you push in on the relay armature that locks it in place. There's a video here: https://www.funwithpinball.com/exhibits/small-boards-page-2#VariTarget

If your Vari Target ever worked properly it's unlikely that the spring is bad. If it won't return under its own power it's more likely that there's some mechanical reason (dirt, grime, too much tension from the contact wipers, rubbing or binding against the frame, mounting bolt is too tight, etc.). Other Gottlieb steppers usually need about 4 turns of the spring for appropriate tension on a clean mechanism. Not sure about Vari Targets though.