About 2 months ago my 1993 Civic VX Hatchback just plain wouldn't start
one day. Took out the battery (7 years old by that point), put in a new
one, started like a champ.

I seldom use the car (3-4 trips a week at most of no more than 5 miles
per). Six weeks after replacing the battery, the car once again
wouldn't start. Wouldn't even turn over. Just got a clicking from the
engine. Interior and dash lights worked fine, though. After a few
attempts at starting, the headlights were weak; I charged the battery
back up and still had the same problem starting. A friend led me
through some testing which seemed to indicate a dead starter. So I
pulled that, got a refurbished one, and put it in.

Now the car still won't start, but has come up with a new failure mode:
When I turn the key to position II, I get rapid clicking from under the
left side of the dash, somewhere above the fusebox. Basic Googling has
turned up a couple posts that suggest the main relay. Any other
possibilities? What testing can I do?

Thanks much,

Sasha