+1 low battery.
+1 battery tender.
Also, aux socket & power cable from powerlet:
http://www.powerletproducts.com/The socket goes into the top rear motor mount.
There's a connector for it on the harness.
Cable is for patching battery tender to socket.
I'd never stopped to ponder why a solenoid will chatter on a low battery, but heard it explained a while back.
The battery has enough juice to activate the relay, which causes a voltage drop that makes it release.
Repeat ad buzzium.