There’s a joke going around the Conservative Conference in Birmingham that speaks to the fear Tories now feel about the possibility of a Jeremy Corbyn-led government.

Whenever they’re confronted by an MSP or a Scottish MP, Tories of an older vintage will say they remember when Scotland used vote en bloc for the Labour party.

Then they thank their Scottish colleague “for imposing Tory government on the UK”.

Ruth Davidson has 'made this conference about her bid to become First Minister of Scotland'. Picture: PA

Scottish Tories would quite like it if the UK party would stop trying to impose SNP government on Scotland. Constant Brexit infighting and the risk that MPs and party members will be putting someone unsavoury in charge terrifies the popular Scots, who would like to get on with winning power themselves without worrying about having to bail out “Prime Minister Johnson” in another snap general election.

With a tilt at Number 10 definitively ruled out, Ruth Davidson has instead made this conference about her bid to become First Minister of Scotland. Her supporters believe that while it may seem unlikely, a Conservative administration at Holyrood is possible.

Going into the 2007 election, the SNP were defending the same share of the vote as the Tories will be in 2021, with viewer MSPs – although their main rivals, Labour, were in a much weaker position than the SNP government is now.

There are two things that it is widely accepted Davidson needs to do if she wants to have a chance of winning the next Scottish election.

Work on the first of those seems to be progressing reasonably well. The party is dominated by Davidson’s image: she is their only recognisable figure in the Scottish Parliament, and it’s doubtful that as many people in Scotland would know who David Mundell is.

The Scottish Tories desperately need to push forward some new talent into the limelight, to build the sense that the party is a government in waiting, rather than a one-woman publicity machine.

That much seems to have been acknowledged. In what has been a Ruth rally at the past few UK conferences, the Scottish Conservative fringe meeting on the Sunday afternoon was handed over by the leader to three other voices – indeed, the Scottish Tory leader slipped out before the end, having only made brief remarks.

Instead, it was Andrew Bowie MP, Nosheena Mobarik MEP, and Donald Cameron MSP who held the floor, and both Bowie and Mobarik delivered uncompromising messages on the need for internal reform if the Tories want to win at any level. Mobarik was particularly impressive for telling a room for of white blokes in sharp suits that too many Tory candidates were white blokes in sharp suits – particularly in Scotland.

The other issue is policy. Davidson keeps reminding Tories that they need a positive message, one that can compete with Corbyn’s promises to young people and goes beyond the divides over Brexit.

Yet despite all the reminders, her party has yet to come up with its own message that goes beyond Unionism and opposition to indyref2.

Cameron is in charge of developing the party’s platform, but that exercise seems to only just be getting under way from the response he gave to a question about whether Scotland could follow a new proposal from Theresa May to tax foreign property buyers more.

He appeared unsure, and the matter had to be referred up to the shadow finance secretary, Murdo Fraser, who duly said the party would look at it. Well, why hadn’t they already? Scotland’s house prices are scarcely any less inflated in places like Edinburgh and Glasgow, and second home ownership strikes a chord with communities in rural areas and heavily-touristed cities.

Davidson is not a details person; she would admit this privately, I’m sure. She is a saleswoman, and she needs a big, bold pitch to sell when 2021 rolls around. Tories in Birmingham have been grumbling that Corbyn stole their majority last year by promising young people “the moon on a stick” – free tuition and nationalised services.

The Scottish Tories should know to grumble less and work out their own offer: in 2007, Alex Salmond pulled the same trick, promising free university tuition and an end to prescription charges. They won’t get much help from London, so the Tories will have to do the hard work to impose themselves on Scotland.

Paris Gourtsoyannis: Hard work lies ahead for Ruth Davidson