Idan Dershowitz discusses the use of אלהם אלהך in The Valediction of Moses; defends text against claim that this is "a practical impossibility in an authentic text."
Idan Dershowitz, The Valediction of Moses: A Proto-Biblical Book (Forschungen zum Alten Testament 145; Tübingen: Mohr Siebeck, 2021), 79-80n13
It has often been asserted that אלהם אלהך is a practical impossibility in an authentic text. For instance: “The expression ‘I am God, thy God,’ is extremely unlikely and would be tautological. ‘Jehovah thy God’ or ‘Chemosh thy God,’ would have a meaning; but this is meaningless” (“Biblical Research: Shapira’s Last Forgery,” The Independent 35 [August 20, 1883], 9). Ginsburg wrongly asserts that “neither does the phrase אלהם אלהך, ‘god, thy god,’ occur in the Old Testament” (The Athenoeum 2911 [Aug. 11, 1883], 179). Besides being obviated by our psalm and others, this argument confuses the concepts of synonymy and homonymy. אלהם “Elohim” is used here as a proper noun, as in the fist chapter of Genesis and countless other biblical passages, while אלהך is the (suffixed) common noun “god.” There is thus nothing tautological about the phrase אלהם אלהך “Elohim, your god.” While one might object to the aesthetics of a sentence such as “She is content with the content,” it is not redundant. Incidentally, parallel arguments have been made for the secondariness of the name Elohim in the Elohistic Psalter, with phrases such as the one in question described as “tautological monstrosities”; these assertions should be similarly dismissed. (See Ziony Zevit, “The Elohistic Psalter,” in The Religions of Ancient Israel: A Synthesis of Parallactic Approaches [London: Continuum, 2001], 668-78, at 675.) Cf. also the Islamic shahada, the beginning of which is commonly translated, “There is no god but God.”