Almost a week on from the US elections and the chin-stroking among the commentariat continues, not least in those heartlands of pondering, the Sunday politics shows.

From Sky News’s Sunday with Trevor Phillips to the BBC’s Sunday with Laura Kuenssberg and BBC Scotland’s The Sunday Show, the question was the same - what does a Trump victory mean for us?

That is not “us” in the shape of the various pundits who turned out to be wrong in their predictions of a win for Kamala Harris. Rory Stewart, chief among the Harris cheerleaders, has not, for example, fallen on his sword at The Rest is Politics podcast.

No, the “us” in question was the UK in general, and the Starmer administration in particular. What would Trump tariffs mean for the UK? Did it matter that so many senior members of the government, including the Prime Minister, had been less than complimentary in the past about the new president-elect?

While chewing through those topics other matters arose, such as who will be the next British ambassador to the US, what Donald Trump thinks of Scotland, and how Theresa May’s Scottish adviser scuppered Nigel Farage’s chances of a job as a special envoy to the Trump administration.

Fiona Hill told Trevor Phillips: “I was sent to Washington last time around to tell Reince Priebus, who was then Trump’s chief of staff, that there was no way in the world that we’d have Nigel Farage in any way involved, and I was happy to give that message.”

May’s team spent a day with Trump in the White House, and Glasgow-born Hill was impressed by his grasp of detail. “Bearing in mind this was only a day after the inauguration, he was on it.”

What was he like, Phillips asked.

“He’s naturally an emotional man. It may well be because his mother is Scottish. We’re all emotional people. His mother is a MacLeod and my middle name is MacLeod. One of the first things he said was, ‘We could be related’.”

Darren Jones, Chief Secretary to the Treasury, was doubling as minister for the Sunday shows, which was fortuitous given the fears about Trump tariffs harming the UK economy.

Well, it would have been lucky had Mr Jones directly addressed the questions put to him. But he would not be drawn on what he called “sensitive hypothetical future scenarios”.

“You’ll have to forgive me, I’m not a commentator, I’m a Cabinet minister,” he told Phillips. “It’s appropriate for officials to plan for different scenarios but you are asking me to comment on sensitive hypothetical future scenarios.”

Nor was the minister ready to say when the government would fulfil its promise of spending 2.5% of GDP on defence.

A date wasn’t given in the manifesto for two reasons, he told Laura Kuenssberg. “The first is that we needed to conduct a strategic defence review, which is happening at the moment and we’ll report in the spring, and the second is because as with all spending decisions, it has to be subject to wider fiscal considerations.”

The person conducting the review is George Robertson, former Nato general secretary and Defence Secretary in Tony Blair’s first government. Robertson is among several Blair-appointed personnel making a “comeback” under Keir Starmer. Alan Milburn, former Health Secretary, is now a government adviser on the NHS. Jonathan Powell, ex-Downing Street chief of staff, was last week named as National Security Adviser.

Peter Mandelson, one of several people being mentioned as a possible UK ambassador to the US, was on Laura Kuenssberg’s panel with journalist Tina Brown and the historian Andrew Roberts. Mandelson is also in the running to be the new chancellor of Oxford University, in competition with William Hague, the former Tory leader, and Lady Elish Angiolini, Scotland’s former Lord Advocate. It’s a busy old time in the world of plum appointments.

Tina Brown said she hoped Mandelson would “dust off his dinner jacket” and become the ambassador. She had advice for him if he did.

“What Brits don’t quite understand,” said Brown, “is that post-Brexit there is a slight sense that England doesn’t matter as much as it did, and you may be seen as the salesman of a distressed asset who has to pound the door to get an interview. You’re going to have to work those rooms very hard in Washington. And please don’t bang on about the special relationship. That is really retired.”

Mandelson said he was more in favour of a new relationship rather than a special one.

So he was up for the job? As if it was that straightforward.

“Nobody has spoken to me about this job. I read about it in the papers but nobody has actually spoken to me so let’s put it to one side,” he said.

Would he be interested if asked?

“I’d be very interested in giving advice about trade to whoever is appointed,” said Mandelson. He went on to praise David Lammy, the Foreign Secretary, for showing “some pretty shrewd judgment” in getting to know the Trump team.

That would be the same David Lammy who once described Mr Trump as "a woman-hating, neo-Nazi-sympathising sociopath.” Mr Lammy told the BBC last week that was now “old news”.

Not to be outdone on the Trump front, BBC Scotland’s The Sunday Show interviewed the Republican commentator and former Trump adviser Jan Halper-Hayes.

Martin Geissler asked what she thought of some of the comments made about Mr Trump in the run-up to the election, and First Minister John Swinney’s endorsement of Harris.

People think that Donald Trump holds grudges, said Halper-Hayes, but look at the way Robert F Kennedy Jr, a previous critic, had been welcomed into the team.

What does the president-elect think about Scotland, Martin Geissler asked.

“If he could move there and golf at his course he’d be there all the time,” said Halper-Hayes.

But the criticism of him, the protests? Water off a duck’s back, she said.

“I don’t know any other public person who could tolerate ten years of being bashed, not age as every other president has aged, to keep his spirit and commitment going, and to keep on fighting. That to me is all we need to understand. It’s not to say it doesn’t tick him off, but he knows he can overcome these things.”

Nothing for any ambassador to worry about, then,  whoever he or she turns out to be.