There are many ways to approach this question. Key here, I believe are your own words (particularly the last phrase), "to collect regional folk tales, or put much effort into analyzing or studying those tales." In intend to use these against you!

The collecting part has been a natural process and has occurred since people began writing things down - a fact you are clearly alluding to! Maybe even before writing this occurred if we consider the possibility that prehistoric forms of art were depicting stories.

Gilgamesh was likely a story in circulation before it was written down. Was, then the person(s) who wrote it down a folklorist? If we rely on the second part of your intuitive (and very good) definition of a folklorist, I think we would have to say no. The Gilgamesh author recorded what was likely folklore, but did not offer analysis of the material.

In the same way, we can find clear evidence of people recording folklore - throughout history. What we know of most ancient mythologies is thanks to the efforts of scribes who recorded oral narratives. Sometimes - rarely - we have an inkling of analysis. The fourth-century BCE Greek writer, Euhemerus proposed (or embraced) the idea that the gods and events of mythology were based on real people and events.

This line of thought echoed over the centuries as a dominant means of analysis of folklore - so we can see that some - a limited some - of analysis was occurring early on. This approach was certainly influential with the Icelandic author Snorri Sturluson (1179-1241) who applied this approach to Norse mythology. That said, does this qualify the proponents of this approach as folklorists? Not in the modern sense, I think, and yet we can see the roots there.

It is also important to point out that many Romans were intuitive folklorists when they evaluated local oral traditions in the far-flung Empire, always seeking to find parallels with their own. This was a type of intuitive comparative analysis of folklore that allowed Romans to understand local traditions, framing them in a context to match or at least to compare to their own. Did this make them folklorists? It comes pretty damn close in my estimation, and yet they and their method lacks generational continuity when it comes to modern folklorists.

If we look at later authors and what they were doing, we can see many medieval authors - Chaucer and Boccaccio come to mind - who were clearly using oral narratives to inform their own work. Chaucer's introduction to ‘The Wife of Bath’s Tale’, includes the character setting the stage as ‘In the olden days of King Arthur [when] … all this land was filled with faerie’. The Wife of Bath adds, ‘This was the old belief’. Here we have a small morsel of analysis - and an intriguing morsel it is! The same problem exists, however, when it comes to generational continuity.

If we fast forward to the sixteenth through eighteenth centuries, we find many more people collection oral narratives. Many of these individuals are lumped together as antiquarians, implying that they liked to collect a variety of things they felt were from the past, but that they didn't necessarily include analysis in any sustained way. Were these individuals folklorists? I think a case can be made to answer yes, because there was clearly generational continuity with scholars we refer to as folklorists. These antiquarians were collecting material, and they were beginning to offer analysis if only a limited ways. Furthermore, they were influencing those who followed.

I suppose the real question can be raised about the antiquarians who were most systematic about what they were doing. A clear quandary exists when we attempt to consider the case of the French author, Charles Perrault (1628-1703). He collected and published a collection of French folklore that reverberated through the decades - and continues to be influential.

Similar roots can be found in the works and influences of the Germans, Achim von Arnim (1781-1831) and Clemens Brentano (1778-1842) who used oral narratives to inform their own poems and stories. They were enormously influential, but they tapped the realm of folklore to create art. Would we think of Disney as a folklorist? Not in the strictest sense of the work.

Nevertheless, von Arnim and Brentano had a direct influence on the Brothers Grimm - and it is with Jacob Grimm that (1785-1863) we can settle on the first person who can clearly be referred to as a folklorist. Why him and not those who went before? The answer is in the second, pesky clause of yours: "put much effort into analyzing or studying those tales." The Brothers Grimm were clearly influenced by Perrault (they even included some of his stories into their first edition of their folktales - 1812-1815). They were also directly influenced by von Arnim and Brentano. In addition, they own much of their methodology and enthusiasm was thanks to the teachings of a historian (of all things!): Friedrich Carl von Savigny (1779–1861).

With clear acknowledgment of the important roots and influences, we generally look at Jacob Grimm who was the first person to systematically collect and begin the thorough, careful analyze of European folklore. This in turn gave birth to the discipline of folklore/folkloristics. The way the field developed in Europe and North America can trace its roots directly to his work. Indeed, without too much effort, many folklorists can trace their intellectual "genealogy" directly back to Jacob Grimm (he is the mentor of my mentor's mentor's mentor!). Before Grimm, it is not possible to trace that direct line of person-to-person influence.

We look to Jacob Grimm in the context of folklore in the same way that we look to Sigmund Freud (1856-1939) and the birth of psychology. Many thinkers considered the function of the mind, the importance of dreams, etc., but it wasn't until Freud that there was an actual birth of the modern discipline of psychology with its systematic analysis and with its generational links from scholar to scholar.