Replying to myself here.

I've fixed the problem, but I don't understand WHY what I did resolved the problem. Perhaps someone else can help educate me.

Here's what I did:

After re-reading Bartamos' good instructions, I realized the best approach was to systematically check everything step by step.

After wiring up the bulb directly to the battery and confirming the bulb would light, I began backtracking to the brake light switch and connected wiring and trying to manually hold positive and ground wires onto a loose bulb.

I determined although the positive wire coming from the fuse box and connected to one of the brake light switch terminals showed 6.04 volts on my multimeter, it would not light the bulb when manually connected to the bulb.

I then unhooked the other wire going into the fuse box and touched it to the bulb and it lit.

I checked the voltage and it showed only slightly higher. 6.18 volts.

After cleaning all the contacts coming into and out of the fuse box, the wire coming out of the fuse box began lighting the bulb again.

After reconnecting all the wires to the brake light housing, it started working again.

Obviously, something in cleaning the connections (all of which seemed tight) and were good enough to pass through 6.04 volts was the difference.

Could that minor voltage difference be the factor?

Thanks in advance for any replies. The wisdom of those who are more knowledgeable is extremely helpful to the rest of us.