The question of the semantics of the verb פָּסַח = pāsaḥ is a difficult one, in part because it so quickly gets lost and subsumed in discussion of the noun pesaḥ (the name of the feast/festival), and in part because the verb has its own inherent difficulties.
There has long been a question as to whether there should be one or two distinct "roots" behind the verb. Brown-Driver-Briggs (p. 820) opts for two, and this is reflected in the discussion by Glasson referenced by OP.
However, the more recent Hebrew and Aramaic Lexicon of the Old Testament (vol. 2, p. 947) has only a single heading under which all occurrences are listed, and which references Glasson's article specifically -- but which glosses it (sub qal 2., with ʿal) as "limp by, pass by, spare", so no "protect".
There are, in fact, only seven occurrences in the Hebrew Bible. The three occurrences in Exodus 12 (vv. 13, 23, 27) are usually grouped with one further instance in Isaiah 31:5 (which is exactly what Glasson does, too):
Isa 31:5 [New Jerusalem Bible] Like hovering birds, so will Yahweh Sabaoth protect [יָגֵן yāgēn] Jerusalem; by protecting [פָּסֹחַ, qal inf. abs.] it, he will save it, by supporting it, he will deliver it.
When this issue gets picked up for attention, the commentaries (I've consulted a few) tend to go over this same ground. William Propp has more to say than most.1 He translates the relevant verses this way:
12:13b (P) And I will see the blood and protect over you, and harm from destruction will not be upon you in my striking the land of Egypt.
12:23 (E) And Yahweh will pass to harm Egypt and will see the blood on the lintel and on the two doorposts, and Yahweh will protect over the doorway and will not allow the Destroyer to come into your houses for harm.
12:27 (E/D-like) "...Then you will say, 'It is the Pesaḥ slaughter sacrifice for Yahweh, who protected over Israel's Sons' houses in Egypt in his harming Egypt, but our houses he rescued'."
In spite of his stilted English, his preference for the "protection" meaning is clear. In his discussion he notes that both the "pass over" and "protect" understandings are ancient ("traditional"), and that his own inclination is wholly determined by context.
So, "how should we understand [pāsaḥ]" (OP)? Good question! In either one of these two ways, reckoning with:
- a fairly limited number of occurrences;
- strong contextual "colouring" -- especially if one begins with the Isaiah text in the analysis;
- traditional association with the verb עָבַר ʿābar (first verb of Exodus 12:13); and
- the antique translation tradition (as noted by OP, and discussed at length by Glasson).2
The lexicographers don't give the clarity that we "users" would like. In the context of Exodus 12:13, it should also be noted that it is not necessarily the case that the "blood" (itself) does the "protecting" -- but that it is explicitly the sign (אֹת ʾōt, v. 13) in this instance -- analagous to the perpetual sign of the "rainbow" (Genesis 9:12-16) -- indicating a protected household. The Lord is both the Destroyer and the Protector (Ex. 12:23).
- W. Propp, Exodus 1-18 (Yale, 1999), p. 401. The supralinear letters in the text citations follow Propp's method for indicating his source analysis.
- One should also add to the bibliography: Sebastian Brock, "An Early Interpretation of pāsaḥ: ʾaggēn in the Palestinian Targum", in Interpreting the Hebrew Bible: Essays in Honour of E.I.J. Rosenthal, ed. by. J.A. Emerton and S. Reif (Cambridge University Press, 1982), pp. 27-34. (Not currently available to me, but if anything turns up, I'll add it in.)