Grammatically analysing "Sahha Ramdankoum!"

Sahha Ramdankoum صحّة رمضانكم!‍ ‍This Darja phrase, which might be rendered as "happy Ramadan!", is familiar to any Algerian. It groups with a few others - notably Sahha Ftourkoum صحة فطولاركم "happy fast-breaking dinner!" and Sahha Eidkoum صحة عيدكم "happy Eid!" - as an example of a not very productive template "Sahha X+2nd person possessive" expressing good wishes on the occasion of X. But what is "sahha" doing in such forms?

In many contexts, "sahha" is a noun meaning "health"; we can be sure it is a noun, since it can be the object of a preposition and take personal possessive endings, as in b-sahht-ek بصحتك "good for you" (with your health). But there is also a defective verb, taking 2nd person perfective endings: sahhit صحيت (to a man), sahhiti صحيتي (to a woman), sahhitou صحيتو (to a group) "thanks / well done" (a little stronger than sahha "thanks"). The expected 3rd person masculine singular form of this verb would be sahh صح or sahha صحى; sahh actually is attested as an impersonal verb (ysahh-lek يصحلك "it is appropriate for you"), but its meaning is sufficiently distant that it's not necessarily part of the same paradigm. So in principle, "sahha" in "Sahha Ramdanek" could be interpreted as a noun, or a verb. Is there any way to decide which?

If it's a noun, then the phrase's syntax is bizarre - the literal interpretation would then be "Health is your Ramadan", whereas to make it fit the actual meaning we want at least something like "Your Ramadan is health", which would be the opposite order (?Ramdanek Sahha رمضانك صحة). If it's a verb, on the other hand, the syntax is fine - subjects in Algerian Arabic routinely follow the verb, and perfective verbs are routinely used to express states, so we could interpret it as something like "Healthy is your Ramadan!" or even, if we allow the perfective to be optative as in Classical Arabic, "May your Ramadan be healthy!"

On the other hand, if it's a verb, then it should agree in gender and number with what follows it, with feminine "sahhat" صحات and plural "sahhaw" صحاو. This can't actually be tested directly: in all such expressions that I can think of, the noun happens to be masculine and singular, and this expression cannot normally be extended to congratulate people on other occasions. But if we imagine using this formula to congratulate someone on their happiness, I for one would much sooner say "Sahha Farhatkoum" صحة فرحتكم than "Sahhat Farhatkoum" صحات فرحتكم, which suggests that my mind, at least, is not analysing it as a verb.

Perhaps it's neither noun nor verb, then? There are a few words in Algerian Arabic that form predicates and comme at the start of the clause, but do not take verbal morphology - for instance, makash ماكاش "there is no" or oulah ولاه "no need (for)". Putting it in this class would take care of the problem, but just leads us to a different one: can this class of non-verbal predicators be given a coherent positive definition, or is it just whatever happens to be left over from defining the major word classes?

Be that as it may, best wishes to all readers for this coming month, and, for those fasting it, Sahha Ramdankoum!