Starter/battery weirdness

[Oregoon]

Alrighty--

With the key off in my '66 Burb, the battery will go stone dead over night, even though nothing appears to be left on. I have no radio, no interior lights (they're missing), and nothing seems to be left in the on position. What's more, my wiring appears to be in good shape, and relatively unmolested.

When I connect my battery (I'm temporarily using a quick-disconnect like one would in a boat), my starter often acts like it's got solenoid trouble--not engaging, clicking, etc. However, after a few tries, it cranks my 292 and I'm off to the races.

I'm going to replace the starter tomorrow, and the battery cables. First I'm going to go bananas with a wire tester, and see what gives...

Anyone have any similar issues? Ideas? Advice?

As ever, thanks in advance.