There is an historical Jesus effort. Is there an historical Buddha effort, and if there is, how can I read about it?
Although much of modern Buddhology involves historical research of later developments in the tradition, there is not, to my knowledge, any scholarly inquiry into Shakyamuni Buddha's historicity even remotely comparable to the current Jesus history studies. There are good reasons for this. In all of Buddhism it is understood that there have been many Buddhas before the historical Buddha Shakyamuni (ca. 6th century B.C.E.), and there will be many other Buddhas in the future. Buddhism's view of its founder does not share the crucial thrological aspect of Jesus' role IN HISTORY held by much of Christianity.
The earlier Pali suttas sometimes have been considered more historically reliable in the West than the Mahayana Sanskrit sutras, some of which were clearly compiled even a thousand years after Shakyamuni's death. However, even the Pali suttas were not compiled for two or three centuries after the Buddha's death, and the earlier Mahayana Sanskrit sutras appeared not very long after the Pali suttas. Even the later Mahayana sutras, and the Vajrayana tantras, claim to be the words of Buddha, preserved esoterically until people were ready to hear them.
We really do not know what the historical Buddha actually said. The relative unimportance of history in traditional Indian culture also has contributed to the lack of reliable historical sources. In Mahayana and Vajrayana Buddhism there are vast pantheons of various buddhas and bodhisattvas in diverse realms who are venerated along with Shakyamuni. Although the historical Buddha is still highly venerated in most (although not all) of these schools, and the story of his awakening is a major paradigm, there is also a strong emphasis on the realization and enactment of awakening in one's own life. There are a great variety of good modern and traditional biographies of Shakyamuni Buddha available, but not with the same level of historical scholarship of the modern Jesus studies.
Is there any serious scholarly effort examining the hypothesis that Jesus left Palestine in his teenage years and studied in India for a number of years and returned to Palestine to begin his ministry?
The idea that Jesus studied in India has been around for a while. But I am not aware of any detailed scholarly work that might confirm this, and I believe that it is unlikely than any such confirmation will ever be found.
According to an Episcopal priest friend and colleague in Buddhist-Christian dialogue, "The Christian scholarly consensus (including the Jesus Seminar) is that Jesus gave no signs of being anything but an enlightened Jewish rabbi: he told stories like rabbis do and tried to strip away false ideas about the holy, and about worship etc."
I would add that there clearly was some ongoing interaction between the Mediterranean and India after Alexander's conquest. One good source on this is the first three chapters of Stephen Batchelor's "The Awakening of the West" (Parallax Press). So there was likely some diffuse influence of Buddhism in the milieus in which Jesus may have participated. Christians, in turn, may likely have influenced the early development of Mahayana Buddhism, and also later as Buddhism spread east on the Silk Road, also traversed by Christians. So we might well see commonalities and parallels between the Gospels and Buddhism without Jesus himself ever having had any direct contact with Buddhism, or with other Indian religious people.
My experience in studying the world's religions is that neither Moses, Buddha, Mohammed, nor any other founder like Joseph Smith ever appear to believers consistently through history (or at all); yet Jesus seems to appear to people (followers and seekers) continually throughout history and continuing today. I have read and heard many others also testify as to personal encounters with Jesus as God and as risen human. What do you make of such encounters and experiences which are different other religions' experience of the numinous and transcendent?
There are certainly many moving accounts of powerful Christian conversion or devotional experiences including visions of Jesus. But to respond from a Buddhist perspective, there have also been many accounts throughout history, to the present, of people who have experienced visions of buddhas, bodhisattvas, and great ancestral Buddhist teachers, and I know that similar events have been reported in other religious traditions.
In much of Buddhism such visions are respected but not considered of ultimate significance. In Zen, for example, such visions are even considered to be a potentially dangerous distraction from the real work. The emphasis of the practice and faith is one's own realization, enactment, and integrated expression of the awakened awareness experienced by the Buddha and others. This is similar to the priority of many Christians to themselves strive to live as Jesus did.