Seeking opinions: lowlander or highlander?

[Karl R]

The family genealogists have been unable to track my great x2 grandfather before he immigrated to Canada. Since his name is William Brown, searching the Scottish census turns up too many results, with no way to rule enough of them out. It's unlikely that we'll be able to get a yDNA test (particularly from my cousin, the conspiracy theorist).

Given the Brown surname, he could be either a lowlander or highlander. From what I can tell, there is a concentration of Browns/Brouns in the lowlands, such as Clan Broun in East Lothian. There is also a concentration of Browns in the highlands, such as the Brown sept of Clan Lamont and the Brown sept of Clan MacMillan in the Cowal peninsula.

Based on what details we have, I'm wondering if it's possible to determine that it's somewhat more likely that he is one, rather than the other.

Name: William Brown
Year of Birth: 1815-1820
Country of Birth: Scotland
Emigrated to: Canada
Year of Emigration: 1851-1856
Occupation (in Canada): Laborer

At the time he emigrated from Scotland, he was a bachelor. It's unknown whether he would have been traveling alone.

Contemporaneously, Scotland was going through both the Second Highland Clearance and the West Highland Potato Famine. But we have no information whether that was the reason for his departure from Scotland. I'm not aware whether there was a comparable movement from the lowlands during those years. I believe the Scottish Lowland Clearance had ended before the 1850s.

Obviously, he could be from anywhere in Scotland. But based on the information above, would you think William Brown was more likely to be a lowlander or a highlander?