I will provide reference to these five Aramaic grammar books:
Caspar Levias, Cincinnati, 1900
Caspar Levias (Hebrew edition), New York, 1930
J. N. Epstein, Jerusalem, 1960
David Marcus, University Press of America, 1981
Elitzur Bar-Asher Siegal, Germany, 2013
I don’t have Rabbi Frank’s English book, but I couldn’t locate your example on a whim in the Hebrew version either (the Hebrew volume is called דיקא נמי). That’s okay, I’ll try to explain some of the grammatical points based on some modern and classic grammar books.
The short answer to your question is that פְּעֵל may be a stative version of פְּעַל, but there are other grammatical designations that grammarians have given פְּעֵל (regarding grammatical case, see Epstein, p. 32, bottom). However, these do not seem to be concrete rules as are the “Binyanim” in their respective designations. Also, this change is not due to a phonetic phenomenon as you correctly surmised; grammarians have only derived rules as to its reasoning, but in essence, it is just an irregularity or corruption present in JBA (Jewish Babylonian Aramaic).
The very way in which verbs function in Aramaic is not a simple matter. Although Rabbi Frank may use the terms “present, past, future” as a given, grammar works of the 20th century have more nuanced definitions. As an aside, I haven’t looked at Frank’s book in depth, but a casual perusal indicates that’s the case. Of note, however, is that Epstein’s book uses the same tense conventions as Frank, and does not appear to address this topic, despite his forebears’ discussions (I assume this is related to Kutscher’s famous critique of the work, but I have not checked).
Marcus (p. 7) and Levias (p. 61) explain that JBA has something which is akin to regular tenses called Perfect, Imperfect, and Participle (Levias calls it the present indicated by the participle). These correspond to Past, Future and Present respectively (similar to Arabic). Beyond the scope of this discussion, is the innovative treatment of TAM [tense, aspect, mood] advanced by Bar-Asher Siegal in chapter 7 (pp. 162ff).
The existence of פְּעֵל does not seem to be acknowledged by Epstein (p. 34) or Marcus (p. 38). However, Levias discusses this (p. 60; Cf. p. 70f; HE, p. 129):
Qal.— §191. The Qal, or
simple stem, consists of the simplest root found in the language. The
3d sing. masc. perfect is קְטַל, especially with transitive verbs.
Beside קְטַל are also found קְטֵיל and קְטוֹל, chiefly with neuter
verbs. The last form is rare. In the imperfect all the three vowels a,
i, u occur even in strong stems.
Levias defines the קְטֵיל as a “neuter verb”. Goold Brown (New York, 1882) gives a definition:
IV. A neuter verb is a verb that expresses neither action nor passion,
but simply being, or a state of being; as, “There was light.”—“The
This definition seems to match that of a stative verb (See https://en.wikipedia.org/wiki/Stative_verb; http://www.jstor.org/stable/20705843).
In his Hebrew edition, Levias (p. 125) adds several more details as regards the nature of the “Qal” verb.
קנט. הבנין הקל בעבר נבנה על שלשה משקלים: פְּעַל, פְּעֵל, ופְעֹל. למשקל
פְּעַל הוראת פעולה יוצאת לאחר או עומדת; ד"מ שְׁקַל, לקח; מרד; והמשקלים
פְּעֵל, ופְעֹל מורים על תכונה ומצב, ד"מ בְּעֵת, פחד; חֲרֹב. המשקל
פְּעֵל מורה על תכונה עוברת; ופְעֹל, על תכונה מתמדת. ברבות הימים ההוראה
העומדת עוברת לפעמים להוראה יוצאת, ונסיונות החיים מלמדים את האדם לראות
בתכונות שהיו בעיניו למתמידות רק תכונות עוברות. בהקשה אל העתיד והצווי
גבולי המשקלים נטשטשו ברבות הימים, ומצאנו עתה פעולות יוצאות לאחר
במשקלים פְּעֵל, ופְעֹל, ופעולות עומדות במשקל פְּעֵל.
His outdated linguistic terminology indicates that, although פְּעֵל may follow certain conventions, i.e. that of neuter verb tendencies, the language as a whole has not been upkept in its rigidness. This is a theme covered by Levias throughout all his books, especially in his sharp comments at the beginning of his Grammar on Palestinian Aramaic.