A'll a'to bahn dahn and 'arken unto 'im
I'll have to to go down and listen to him.
corrected after comment from Kiloran_speaking from my original interpretation, from 'I'd like to' to 'I'll have to'
'arken/harken/hearken in this sense is 'listen'. It's not a past tense form of hark, though it looks like one.
I have [had: see below] absolutely no clue on the etymology of 'bahn', but being a native Yorkshireman myself I can use a little extrapolation of speech I do know.
There is a phrase, "Are we baht?" which means 'shall we go?'. It doesn't mean 'about', it definitely means 'go'. This is reinforced by the joking extension of the sentence to "Are we baht baht?" meaning, 'Are we about ready to go?'
From this, I'm making the not inordinate leap to 'bahn' being from the same root. There is the potential that 'bahn' really should mean 'going' rather than 'go' but I'm not taking Sellers' attempt at Yorkshire as being 'direct from source'.
A thought is that it could possibly be tied to 'bound' in the journey sense, as in Bradford-bound, or 'The ship left harbour, bound for the New World'.
There is potential confusion, in that 'baht' can also mean 'without'( On Ilkla Moor Baht 'at = On Ilkley Moor without a hat), but I think context eliminates this.
…and, having now read the Wikipedia link to Ilkla Moor - it actually gives a reference to 'bahn' itself in an alternate lyric, & confirms it to mean 'going'.
From the Lyrics section
Many sources give the first line as "Wheear wor ta bahn when Ah saw thee?" (Where were you going when I saw you)…
In this form, it feels like a much better connection to the word being from 'bound'. 'Where were you bound when I saw you?'
Oddly, though Sellers says his family were from Bingley [just outside Bradford, which is where the Alhambra is], the accent he uses is much more like Parkinson's own Doncaster/South Yorkshire, which has hung onto some of these old speech forms much longer than the rest of Yorkshire. I would imagine in the time of Sellers' youth, some of these forms were more widespread. My own father, born in the same decade as Sellers, kept many of these forms after younger people [and even my mother, who came from a slightly more 'well-off' background] had stopped using them.
There is little doubt that the overall speech pattern is at best what I'd call 'tourist Yorkshire' rather than 'real'. No-one would ever say t'Alhambra. It's a mis-hearing and then oft-used misquote of the Yorkshire glottal stop. The only way perhaps to spell it is with the t-apostrophe, but no-one in Yorkshire pronounces it that way.
For sake of completeness, and as it cropped up in comments above, the precursor is
I hear our Willie's appearing at t'Alhambra.
So I said 'Aye.'
A late thought and perhaps tenuous link. There was a lad I used to work with, who earned the nickname Barnaby, because if ever asked something like, "Are you gonne be in't pub tonight?" would invariably reply, "I'm bahn a be." [I'm bound to be.]
These days, it reminds me somewhat of Groot;)