This is a guess, since I don't have any books with me (beg pardon).
I think he probably grounds the principle of Ruling-Elder in the "rulers of the congregation" (e.g. Ex.34::31) and "rulers of the synagogue" (e.g. Mk.5:22). The people of God were "represented" in councils, absent or alongside an office of divine appointment: be he judge, prophet, etc. Ex.4:29 shows that these predate Moses in his role; the roles surely grew out of the patriarchal roles, and were perpetuated beyond the introduction of Moses (judge/prophet) see Num.1, and were distinct from the subordinate judges he appointed out of his office, Ex.18:17. 1Sam.14:45 shows that the "will-of-the-people," that should be expressed by their representative leaders, was a recognized check on human folly in office--even the highest human magistrates were not to be unaccountable.
It is this "difference in direction" of power that (iirrc) Hodge emphasizes in his discussion of the division of church power. The Minister (which I think he understood referenced by the NT "presbyteros" and "episcopos"), i.e. Teaching-Elder, though he is selected and approved by the people, the seat of his authority is in the Head, even Christ who holds all the offices and distributes his own gifts. The Minister thus does not represent "the will of the people" as such.
Those whom we call elders, i.e. the Ruling-Elder, have the seat of their authority in the Body. They are the proper expression of the motives and heart of the Body. Of course, they are personally under the direct reign of Christ and the Bible is the source of their wisdom. But they come to the session bearing the special concerns (as it were) of the Spouse.
I agree with Hodge on quite a bit of his teaching on church-power. And the OPC (whence I serve) significantly mirrors much of his thought in our 3-office polity. My main disagreement with him is the idea that the NT only uses the term "presbyter/bishop" for the Minister, and thus has said little directly to the Ruler (Elder), for example in qualifications (1Tim.3 & Tit.1). I disagree with him, if he proposes that the Ruler is subject to these expectations in less fullness than a Minister; or even that these expectations devolve to his office as a logical consequence, rather than being directly addressed to it. I agree with L.Wilson that in fact the qualifications for the Minister are rather shot-through the whole of the Pastoral Epistles. The "listing" of qualifications, then, for the ordinary elder/overseer (Ruler) we might think of as minimum standards those elders must be. On this reading, the list is actually less than what is demanded of Ministers (who must themselves first meet this minimum!).
But as to the contrasting directions of church-power, I think Hodge is completely correct.