I've some to a point in my course where I think I have encountered the first use of the passive verb, but I am unsure.

"Tá jíons á chaitheamh ag an mbean ard."

Does this mean, roughly, something like, "Jeans are worn by the tall woman?"

Word for word, it seems to go like:

Tá = be/is/present tense verb

jíons = jeans

á = present progressive verb like "being"

chaitheamh = "worn" (with lenition)

ag = by (in the context of this sentence)

an = the

mbean = woman (with eclipses)

ard = tall/high

No this is not a "random question," but is my translation of this correct? Thanks in advance.

Jeans are being worn by the tall woman is the translation.

á = ag a = At his/its

Literally:
(A pair of) Jeans is at its wearing by the tall woman.

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The dialect I use is Cork Irish.
Ar sgáth a chéile a mhairid na daoine, lag agus láidir, uasal is íseal

Tá sé ag mo bhualadh/do mo bhualadh (at my beating or to my beating).

dom'bhualadh
dod'bhualadh
dá bhualadh
dá bualadh
dár mbualadh
do bhur mbualadh
á mbualadh

'Tá sé ag bualadh mé' is non-optimal!

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

These are all etymologically from ag+preposition. See the comments by John Donovan in his 1845 grammar deprecating the tendency for people to confuse it with do. Go do in Conemara Irish derives from ag+do originally - and has nothing to do with the fact that do is pronounced go in Conemara Irish.

The Munster forms are:

am bualadh (b delenited owing to labials)
ad bhualadh
á bhualadh
ár mbualadh
úr mbualadh
ár mbualadh

The Connacht forms are:

go mo bhualadh
go do bhualadh
ghá bhualadh
ghá mbualadh
ghá mbualadh
ghá mbualadh

The Ulster forms are:

(a) mo bhualadh
(a) do bhualadh
á bhualadh
ár mbualadh
(a) mur mbualadh
á mbualadh

The CO forms are not used (and have never been used) anywhere.

I know. That's why I had to look the 4th and 5th up as possessive forms are so similar in Connacht. However, if someone looks up a grammar book, what are they likely to find?

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___