AS adverts go, it isn’t going to win any prizes for style or wit. But as Green MSP Patrick Harvie observed at Holyrood the day after Theresa May’s Brexit plan was out to the sword by her own MPs, the epic dysfunction at Westminster is one hell of an ad for independence.

It’s certainly not much of an argument for more of the same.

There’s so much bad faith for one thing. Mrs May, a Remainer, pushes a policy she doesn’t believe in, up to and including No Deal. Jeremy Corbyn, a lifelong Eurosceptic, tries to hide his attraction to Brexit because his party is overwhelmingly Remain. And Nicola Sturgeon calls for a People’s Vote, not because she expects it to reverse Brexit, but because she expects it to deliver it.

As I’ve written before, the First Minister’s conversion to a People’s Vote last autumn is a curious one.

A second referendum on Europe would displace a second referendum on independence within the current Holyrood parliament. An EU vote would take so long to hold, there would not be enough time to follow it with an independence vote before the 2021 Scottish election.

Not only that, if a People’s Vote killed Brexit, it would negate Ms Sturgeon’s mandate for Indyref2.

The SNP’s 2016 manifesto said Holyrod should have the right to hold another referendum if “there is a significant and material change in the circumstances that prevailed in 2014, such as Scotland being taken out of the EU against our will.” No Brexit, no Brexit-based mandate.

So why would Ms Sturgeon miff her supporters - including some of her MPs - by championing a policy that seems to thwart her core aim?

There was a clue the day after Mrs May’s defeat. “A second referendum [on Bexit] would not guarantee Scotland’s wishes will prevail,” the FM wrote in the Herald. Quite so.

Indeed, I understand Ms Sturgeon and her advisers think there is more than a fair chance a People’s Vote would deeply disappoint Scotland. In this scenario, there is even greater support for Remain in Scotland than in 2016, but it is thwarted by another UK-wide vote for Leave. At which point, the calculation is that the scunner factor goes off the scale.

Ms Sturgeon could then point to Scotland’s people being ignored not just once, but twice, and ask if they fancied something different.

As the UK government would block an immediate referendum - one constitutional crisis at a time, thank you - she could seek a fresh and unambiguous mandate in 2021.

But playing the long game - ‘from gung-ho to go-slow’, as Kenny MacAskill acidly puts it - means facing more pitfalls and opponents.

“It would be unconscionable to kick the can any further down the road,” Ms Sturgeon harrumphed after Mrs May’s Brexit defeat. But the FM is also a serial can-kicker.

After prematurely calling a referendum in March 2017, three months later the SNP’s election losses forced her to postpone it with the promise of a revised “precise timescale” by autumn 2018.

Since then, that precise timescale has been lost in the Brexit fog.

On Wednesday, in her latest delay, Ms Sturgeon said there would be an update in a “matter of weeks”. Her spokesman later revealed that meant it was merely expected before July.

I know a week is a long time in politics, but come on...

The vacillation Ms Sturgeon deplores in Mr Corbyn is visible in her too. The wider Yes movement started to lose patience last year, organising huge rallies off its own back, chivvying the party that used to lead it.

Alex Salmond is also urging action. Riled up by his legal win against the Scottish Government, he is off the leash, irritably telling his successor via the media to use the Brexit crisis to secure independence.

Ominously for Ms Sturgeon, this personal feud is fusing with the political row over Indyref2 timing.

There is also the daily experience of a People’s Vote to consider. It is not just the result that people would remember, it is the oppressive grind of the campaign. With the far right ready to jump on the Brexit betrayal bandwagon, a People’s Vote could become the Rancid Referendum, with months of ugly, divisive politics and family and workplace tension. Would that enhance the appeal of re-running the independence vote?

There are now five inquiries into the sexual misconduct allegations against Mr Salmond and the SNP Government and Ms Sturgeon’s response to them. Any one of them could send a curveball the FM’s way. The Holyrood inquiry is particularly tricky. MSPs are expected to mothball it until the police finish their work of the allegations, and then restart it.

That could take it into 2020, even 2021. Ms Sturgeon’s conduct is likely to be under the microscope just as she’s trying to sell a second referendum in the run-up to the election. You can imagine her opponents raising the process during every debate and hustings. ‘How can we trust you on this, when we’ve learned about X?”

Meanwhile, the brute instinct for self-preservation that inquiries bring out is likely to make relations between the warring Salmond and Sturgeon camps even nastier.

Brexit is no advertisement for Westminster. But in the long run, Ms Sturgeon and a split SNP may not be not much an advertisement for an independence vote either.