S. R. Faruqi:

la;T-pa;Te = a turban of which the ends hang down on both sides
saa;xtah = artificial, invented

In this verse several words are noteworthy. A cloud is called abr-e qiblah when it would be very thick and dark. Through the affinity of qiblah he has alerted/shamed the Shaikhs-- 'If nothing else, respect the fact that this cloud has come from the direction of the qiblah , or is associated with the qiblah '. But the Shaikhs are not 'people of the heart' or rakish people-- how in the world will they be intoxicated? Thus he has instructed them to adopt a fake/imitated intoxication and madness, so that there would be some regard and respect for the abr-e qiblah .

By la;T-pa;Te is meant 'carelessly, relaxedly intoxicated', as if the turban would be tied in such a way that it would show carelessness, rakishness, and intoxication. A light, small turban is called a ta;xfiifah ; it was probably popular among young men. This word appears in the 'Dastan-e Amir Hamzah' too, and Mir has used it a second time in this same divan [{1716,5}]:

ta;xfiife shamle pairahan-o-kanghii aur kulaah
shai;xo;N kii gaah un me;N karaamat ho to ho

[a light turban, fancy turban-ends, a robe and comb and cap--
if the Shaikhs would have any place among these, it would be only by a miracle]

The word saa;xtah in the sense of 'artificial' we know mostly because of Ghalib:

G{206,4}.

If we read Mir then we learn that Mir was the first to use this eloquent word. He has versified it in one more place as well, in the fourth divan [{1474,3}]:

mast nahii;N par baal hai;N bikhre pech gale me;N pag;Rii ke
saa;xtah aise big;Re raho ho tum jaise madh-maate ho

[you are not intoxicated, but your hair is tangled; your turban-twists are around your neck
you remain artificially disarranged in such a way, as if you would be intoxicated]

On Ghalib's verse there's a slight imprint of Mir's verse, but its sneakily sarcastic tone and masterful harmony are Ghalib's own.

FWP:

SETS == HUMOR; IDIOMS
MOTIFS
NAMES == SHAIKH
TERMS == IDIOM

Apparently the coming of the dark, heavy cloud is a sign of the arrival of the monsoon, the traditional South Asian season of romance. By evoking the idiomatic, seemingly religious name of abr-e qiblah (while still disrupting the idiom by inserting siyah ), the speaker claims that the Shaikhs, as religious figures, have a duty to offer it proper attention and regard. But the form this regard should take is unusual: the Shaikhs are enjoined to show at least an affectation of rakish, romantic, Sufistic intoxication.

They are to be fake rakes, in other words; they are supposed to act 'beside themselves' in a very self-conscious way. The speaker so deeply assumes the superiority of 'intoxication' and (religious) self-surrender that he enjoins it even when it is fake, and even when no real religious occasion calls for it. Part of his point is surely that the Shaikhs' religious behavior is not heart-felt but rule-bound and hypocritical anyway, so they might as well follow 'Sufistic' rules as any others-- and it would be amusing to see them perform such (for them) absurd behavior.

Mir never has a good word to say to or about the Shaikh, and loses no chance to abuse or sneer at him. This verse is just one more example out of dozens and dozens. See the 'Names' page for many more.