I found it! Well, not the actual pot of gold, but I think I know the origin of the mythical pot of gold at the end of the rainbow.
I've seen this phenomenon twice, once on a pre-dawn drive through Franconia Notch, New Hampshire, and once after my morning jog at Mine Falls Park in Nashua, New Hampshire. That second time, I saw two "pots of gold!"
Remember what a rainbow is, and consider what creates the "end" of the rainbow.
A rainbow is a spectrum of sunlight reflected in droplets of water suspended in the air. It is always a segment of a circle, located 40 to 42 degrees away from the line directly down-sun from the observer. That is, the inner blue part of the rainbow is 40 degrees away from the shadow of your head, and the outer red part is 42 degrees from the shadow of your head.
Now, if you are observing from a height that does not cast a shadow on the air where the droplets are, you can see a full-circle rainbow. Sometimes, the rainbow you observe from the top of a waterfall has no "end" at all.
But if a shadow falls on the water droplets, such as the shadow of another cloud, the rainbow ends abruptly at the shadow line. Nothing remarkable there.
If you are standing under the shadow of a dense cloud, but the sun is shining on a more distant, less dense area of water droplets, you can sometimes see a portion of a rainbow in the distance, which ends abruptly at the edge of the overcast. This can be striking, but there's no "pot of gold."
The most classic view of the rainbow is when you see the spectrum in raindrops right down to the ground. The rainbow ends abruptly at the ground, but there's no "pot of gold" to be found. (And of course, if you move toward the apparent end of the rainbow, the rainbow moves with you, so you can never reach the pot of gold anyway.)
The rare phenomenon that leads to the visible "pot of gold" is when the rainbow ends at the shadow of the earth itself. If the sun is below the horizon but illuminating water droplets in the sky above and down-sun from you, you can see a rainbow that ends in the middle of the sky, but the end is somewhat amorphous and not abrupt at all.
In these cases, the spectrum is distorted, because those water droplets that are reflecting the light from a partially obscured sun do not have the full spectrum of color to reflect. The rainbow ends in a glowing golden disc, somewhat like an indistinct reflection of the sun sitting on the edge of darkness where the clouds are fully shadowed. It looks very like the cartoon depictions of the glowing "pot of gold."
I've seen this twice. One morning in the mountains, the eastern sky was clear, but there was rain in the west. Not long before sunrise, a rainbow appeared in the west, with a glowing "pot of gold" at its northern end. In this case, with the sun below a clear horizon, the "pot of gold" was quite brilliant.
More recently, in Nashua, the entire sky was full of broken clouds, but a full-arc rainbow appeared in the west with a "pot of gold" at each end. This time, the "pots of gold" were less brilliant than the first time, probably because the general cloud cover made the sunlight less brilliant, but they were unquestionably there.
Yes, sometimes there is a pot of gold at the end of the rainbow. But you can't have it. You can only marvel at it for a little while.