Hi Arnie991,
It is possible that no Arnott tartan exists. I might venture to guess that your Arnott family were maybe not natives of Argyll but possibly brought in by the Duke of Argyll from some other area. In the 1700s and later, the Duke tried to improve Argyll by starting up industry and so he brought people from other parts of Scotland into Argyll to teach useful trade skills to the local population. My Patersons were reportedly cheese-makers from Ayrshire originally.
You might want to search the pages of the official Register of Scottish Tartans.
https://www.tartanregister.gov.uk/index.aspx I would add this - beware of those websites claiming to have a tartan, a scroll, badge and plaque for every name. They just want to sell you something and you are not guaranteed to have anything authentic to show for your money. Those businesses are a particular pet peeve of mine!
If you cannot find Arnott tartan, you could wear another tartan connected to your family. Do you know of any other Argyll or Highland family connections to your 4x great grandfather?