Having managed to access Otzar Hachochmah, I'll add some information to @Oliver's answer:
Yehudah Leib Fleischer writes in his essay "Kamah Chachamim Hayu Lanu Bashem R' "Avraham Hachozeh"?" (How many sages did we have with the name R' "Avraham Hachozeh"?, Chorev Vol. 11) that we know of five mentions of Rabbi Avraham Hachozeh:
- In the book Masa'ot Rabbi Binyamin MiTudela (pg. 45):
"Thence it is five parasangs to Tiberias, which is situated upon the Jordan, which is here called the Sea of Chinnereth. The Jordan at this place flows through a valley between two mountains, and fills the lake, which is called the Lake of Chinnereth; this is a large and broad piece of water like the sea. The Jordan flows between two mountains, and over the plain which is the place that is called Ashdoth Hapisgah, and thence continues its course till it falls into the Sea of Sodom, which is the Salt Sea. In Tiberias there are about fifty Jews, at their head being R. Abraham the astronomer, R. Muchtar, and R. Isaac. There are hot waters here, which bubble up from the ground, and are called the Hot Waters of Tiberias. Near by is the Synagogue of Caleb ben Jephunneh, and Jewish sepulchres. R. Johanan ben Zakkai and R. Jehudah Halevi are buried here. All these places are situated in Lower Galilee.
"R. Abraham the astronomer" is how this translation decided to translate "Rabbi Avraham Hachozeh".
A kinah attributed to him: "Tzion k'chi kol tzarei Gilad Letziraich" (see NLI link in the OP).
A piyut from a manuscript in the Bodleian Library (MS Canonici Or. 82, pg. 45v-46r).
Mentioned in the book "Chochmat Hanefesh" by Rabbi Elazar ben Rabbi Yehudah of Germaiza (see OP and Oliver's answer. Note: The Roke'ach quotes two sections from Yesod Morah: From the 7th and from the 10th).
Mentioned by Rabbi Avraham ben Azriel in his book "Arugot Habosem":
"...ור' אברהם החוזה כתב כי ה' הראשון דבק עם ויקרא, כלומר, ויקרא ה'..."
Translation: "...And R' Avraham Hachozeh wrote that the first Hashem is tied with Vayikra, meaning, Vayikra Hashem..."
Fleischer brings the view of David Kaufmann that shows that indeed Ibn Ezra wrote this explanation in one of his books, but in the name of Rasag. Fleischer explains that this doesn't null the view that Ibn Ezra and Rabbi Avraham Hachozeh are one and the same, because there are multiple examples in which rabbis quote certain ideas in the name of other rabbis, even though the latter clearly state they disagree with those views. He notes, however, that Kaufmann could only prove that the Rabbi Avraham mentioned by the Roke'ach and by Rabbi Avraham ben Azriel is the Ibn Ezra, but not that in the other sources. He then sets out to attempt to do this:
About the kinah "Tzion K'chi", there's some basis to attribute it to Ibn Ezra: a. It's written in the Arabic metrical system with "long" (תנועה) and "short" (יתד) with the following form: two longs, one short, one long, one short, two long, one short and two long, which is a meter that Ibn Ezra brings in his book "Hatzachut" as a legitimate meter that he and others have used. b. This kinah was placed among the kinot of the 9th of Av right after "Tzion Halo Tish'ali", by Rabbi Yehudah Halevi, who was a contemporary and close friend of Ibn Ezra. c. Ibn Ezra was a poet and an astrologer, just like Rabbi Avraham. d. The author of the kinah uses terms similar to those used by Ibn Ezra in his "Sefer Ha'ibur" and "Igeret Hashabbat" (related to astronomy and calendrical calculations). e. The author of the kinah wrote "From Eden, the place of all that's precious, came out your rivers", which means that there are two rivers in Eretz Yisrael that come out of Eden, and it seems that only Ibn Ezra held the view that two of the four rivers of Eden come to Eretz Yisrael. f. It's possible to find some hint of this in the last stanza of the kinah where it says: "לראות בזיו זהרך שלום יהי לך ורוב שלום לעזריך", which is almost Ibn Ezra's name (Avraham Ezer).
The piyut "Avi Re'eh" is written in a metric form of two long, one short, two long. This is also a form brought by Ibn Ezra in "Hatzachut" among the customary meters.
Fleischer notes that despite all of this, it's hard to imagine that these were written by Ibn Ezra, because they're so different in content and styling from his usual poems. For example, Ibn Ezra usually inserts many terms from verses in Tanach, and that's not found in these two.
- On the Rabbi Avraham Hachozeh mentioned by Rabbi Binyamin of Tudela: In Fleischer's view, this person couldn't have been the Ibn Ezra. Fleischer believed that by the time Rabbi Binyamin reached Teveria, the Ibn Ezra was no longer alive: From Teveria, Rabbi Binyamin travelled through various locations until he arrived in Mosul, 24-25 days' journey from Teveria. Mosul at the time was ruled by Sayf al-Din Ghazi II (Rabbi Binyamin mentions a Rabbi Yosef Brahan who was an astrologer to King Zun al-Din II), who only began ruling in 1170, while most scholars believe that Ibn Ezra died in 1167 and Fleischer himself thinks he died in 1164. Even if we were to say that Rabbi Binyamin rested in Teveria for a whole year (it's conceivable that he occasionally took long breaks from his long journey), that would still bring us only to 1169, at least two years after Ibn Ezra's death. Furthermore, both Ibn Ezra and Rabbi Binyamin were originally from Tudela. It would be odd that Rabbi Binyamin would refer to a fellow cityman by an odd title, when all over the world he was referred to as Ibn Ezra or Rabbi Avraham Ibn Ezra. Finally, there's not enough evidence that Ibn Ezra ever lived in Eretz Yisrael.
Fleischer concludes therefore that in four of the five references - these are likely referring to Ibn Ezra, although there's still some room for debate about the kinah and piyut, while with Rabbi Binyamin's reference - this is most likely referring to someone else.
Shraga Abramson in his essay "Navi, Ro'eh and Chozeh - R' Avraham Hachozeh" ("A prophet, a watcher and a seer - R' Avraham the seer" (Sefer Yovel - R' Mordechai Kirschblum)) explains that in the past, the titles "Navi", "Ro'eh" and "Chozeh" were reserved for the wisest of Torah sages all over the the world. They were not meant to suggest that these men were actual prophets, but that they were men of great stature. A couple of examples: a. The First Ra'avad in "Sefer Hakabbalah" writes: "...והיו בנרבונא חכמים גדולים...ר' יעקב הנביא גאון בר' משה בר' אבון..." ("...and in Narbonne there were great sages...R' Yakkov the prophet the gaon, son of R' Moshe, son of R' Abun..."). b. Rabbeinu Tam in an answer to R' Meshulam, refers to Rashi as "וכמו שפי' נביא לבב חכמה" ("and as explained by the prophet, the wise of heart...").
Most of the essay is dedicated to explaining the meaning of these titles and bringing many examples, but later Abramson discusses Rabbi Avraham Hachozeh. He analyzes several sections of Arugot Habosem and shows that teachings of Ibn Ezra appear in several places, not just when Rabbi Avraham is mentioned. He also shows the original sources of these teachings, within the Ibn Ezra's writings.
He concludes with saying that it's doubtful that Ibn Ezra was ever referred to as "hachozeh" merely because he was learned in astrology, but rather, more likely, that it was a form of rhetoric employed by talmidei chachamim to express admiration towards the person given the title. As for seeming references to calendrical calculations in the piyut by Rabbi Avraham - he believes that these are doubtful and were probably just a form of rhetoric by author.