Just on parts of the west coast of Scotland - much of mainland Scotland spoke the Scots language, with the (now dead) Norn language spoken in the northern areas (with Norse heritage), and other languages in the border areas. The promotion of Scottish Gaelic as a "national language" is very much modern-day myth-building.
The dialect is arguably alive in some locales, including some places northern Ireland.
To me, the dividing line is code switch. There are rural pubs and such where people will noticeably switch to standard English when speaking to non-locals.
Ulster Scots, it is sometimes called.
Hard to draw distinct lines, especially since the "standard" English near Scots speaking locales is not very standard. Glasgow, Newry and whatnot have pretty quirky "standard" English.
That said, an average person from Newry won't code switch. If you can't understand the accent, they'll just speak loader, slower and more directly at your forehead.
To me that makes it "not a dialect."
What was interesting is that people from a farming background had a very different accent to folks from the coastal fringe - even though they might only be living a couple of kms away!
And to the original point, neither Shetland nor the Scottish Borders have ever had any Gaelic influence at any point in their history, and recent attempts to claim otherwise tend not to go down too well with the locals.
Cumbric? At least until the victory of Anglo-Saxon languages there three or four centuries after the Roman withdrawal.
So yeah, not quite (modern) Scots Gaelic but part of the same family of languages. And not at all recently, but potentially hundreds and hundreds of years of language contact in domestic and community use in some parts, as early Scots was first forming out of a continuum of Northumbrian English dialects.
It's basically "pre-history" in terms of academic discipline, until the high medieval. There just aren't historical/written sources.
What is known comes from third party accounts and relates more to current political happenings than language, history and whatnot.
A Saxon scribe describing the politics of Scotland with 3 sentences of Latin doesn't tell you much about Scottish peasantry.
Even into the early modern, it's pretty hard to know what's happening with spoken dialects.
We know Romans used "Scot" referring to Gaelic speakers, the language spoken throughout Ireland.
We know that 1000 years later Constantine, the product of Pict-Scot marriage declares a united kingdom of Scotland. We know that proto-english, danish, Gaelic and (presumably) Pictish were spoken. What writing exists is usually in Latin.
That said... who knows. The academic "best guess" is not necessarily a good guess.
So yes... Pictish might be closely related to Welsh. It might have been a totally unrelated language. It might not be a language at all.
Also there's a lot of baggage. Ideas from shaky 18th century sociology might be crucial to modern identity.
The idea of Scotland as a uniform "Gaelic kingdom" is a highly political one today.
We tend to think genealogically about these things. I said "Scots is descended from northumbrian" and that Ulster Scots is spoken in NI. But irl... dialects are porous. They don't really "descend."
In any case, I believe that most of the language influence is from the borderlands and the glasgow area. That said, 400 years is a long time... especially considering how young English is.
Not being familiar with that term I looked it up [0] and was surprised by how familiar much of the vocabulary sounds to me, and i'm from south west England... I recognize a number of these words from my childhood (although not so much these days), and many others feel more like an natural accent transformation of a standard english word (although I suppose that might not be the etymology). Admittedly a good chunk of them are completely alien to "standard english" and whether you recognize them or not is more to do with exposure.
[0] https://en.wikipedia.org/wiki/Northumbrian_dialect#Vocabular...
In East London my parents' generation sometimes said "gissa dekko" aka "give us a dekko" aka "give us a look" - but the dekko there came from Hindi, "dekho" (देखो) meaning a casual look or a look-see.
This is how some US teenager, who didn't speak a lick of the dialect, ended up being the lead contributor to the Scots Wikipedia:
https://www.theguardian.com/uk-news/2020/aug/26/shock-an-aw-...
According to my father, who's an Ulsterman, back in the 70s and 80s you would still find job advertisements written in Scots, as supposedly it was a legal requirement to write in both English and Scots - similar to Quebec with English and French. Although most of the time these postings would be complete gibberish as no one who lived in Belfast understood Scots at all.
My understanding from School of was that it went straight from the Brythonic to the Germanic.
The demotion of the Scottish Gaelic language is ignorant assertion. Stop listening to it and educate yourself.