A single click from the starter solenoid with each key turn on my Ford F150. Battery is fully charged. Starter and solenoid bench tested good. What diagnostic steps do you recommend for a shade tree mechanic pursuing the cause?

Swapped out the existing starter in January 2014 after the first incident of
the "click but won't turn over" syndrome. Resolved the problem for 6+
months.

Thereafter, when the problem repeated, it always seemed to occur in wet
conditions, during or after rain and with water on the road. On five or six
occasions, I pulled the replacement starter and had it tested, always tested
good. As soon as the starter was reinstalled, truck would immediately turn
over and start. It got to the point where my son and are were fairly handy
pulling the starter, and if it happened, I'd just drop it and reinstall it without
testing and the truck would start.

Now, however, it happened again. Starter bench tests fine. Battery was at
about 450 amps and recommended amps according to the tech was 525
minimum. Did an overnight charge and it tested fully charged. "Click but no
start."

I'd like to figure this out. I'm not sure in the connection to moist conditions
was mere coincidence or bears any significance. We bought the truck in
December 2013 and it is otherwise a great vehicle. In different life
circumstances, I'd drop it at the local garage and have them figure it out.

Ideas on diagnosing the cause?