It's the North Caley League, level below Highland League, that they were planning joining.
http://www.leaguewebsite.co.uk/northcaledonianfa?forceTheme=true&theme=Bootstrap
Ross County, Caley etc reserve teams used to play in it back in the day.
As I said previously, (I'll keep plugging!!), my home team is reviving to play in that league and are currently fundraising.
http://www.stduthusfc.co.uk
edited to add, I've just been told that the Inverness Thistle team is just a renaming of the Scotrail team that play in the Inverness and District Amateur Premier League.