Scottish First Minister Nicola Sturgeon, a strong opponent of Brexit, has said she will set out her thinking on independence plans later this month.
The issue presents voters and leaders north of the border with another source of dispute, something that this week's decision to delay Britain's departure from the European Union has done little to resolve.
The government is "absolutely committed to an independent Scotland in the European Union," Scottish Minister for Europe, Migration and International Development Ben Macpherson told AFP while out campaigning in Leith, east of Edinburgh.
But even independence backers are divided over Brexit -- five years on from Scotland's own referendum in which 55 percent opted to remain a part of Britain.
Retiree Phil, enjoying the sunshine in a central Edinburgh park, said he wanted "complete independence".
He said he would even consider voting for Nigel Farage's new Brexit Party -- much to the consternation of companion Lisa.
"I'm Scottish first, then European," she said.
Some pro-EU voters who wanted to stay in the United Kingdom in the 2014 referendum are now in favour of independence, but the issue risks pushing away those who want a clean break from both London and Brussels.
Former SNP deputy leader Jim Fairlie said the government's policy of independence within the EU was an "oxymoron", and that tying the two issues together meant "they're not going to get the votes of traditional nationalists like me."
"All the SNP has to do to keep the independence movement together is to decouple it from membership of the EU," he added.
But over 60 per cent of Scots voted to stay in the EU, and some are being won over to the independence cause.
"I know quite a lot of people... who voted to stay with the UK... who now say because they're sick of all the Brexit, they've changed their minds," said local resident Mary Cryan amid the hubbub of Edinburgh's Royal Mile, in the shadow of the city's centuries-old castle.
The shifting blocs have largely cancelled themselves out so far, with polling stuck at around 55 percent versus 45 percent in favour of staying in the United Kingdom, according to polling expert John Curtice, from the University of Strathclyde.
But independence supporters think that the chaos in Westminster could shift the balance.
"It certainly makes the democratic case easier because it really does throw into stark relief this democratic deficit problem," Kevin Pringle, a former director of strategic communications for the SNP, told AFP in his Edinburgh office.
Independence supporters still face a stiff challenge in winning over more conservative voters, who wanted to stay in both the EU and the UK.
"The SNP should concentrate on the day job rather than looking at independence," 50-year-old public servant Craig told AFP in the city's Scots Guards Club, as pipers and other folk musicians played in the background.
Complicating the task for the SNP, Brexit has become something of a moving target since the terms of the withdrawal and the date are far from certain.
"It's a bit like a mirage in the desert," Pringle said.
Key to the calculations will be whether Britain will remain in the European customs union after Brexit or not, which would take any volatile "hard border" debate out of a future independence campaign.
Campaigners must also soon must also find a united position on a raft of economic issues, including what currency an independent Scotland would adopt.
Pringle added: "It's a challenge that can be achieved but I don't think anybody underestimates the scale of it".
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