I now know, as explored in previous tweets, is that there was a least one oil painting of Nathaniel Gow that was gifted to the Birnam Institute in 1929. There was also a painting, perhaps the same one, by John Syme that is said to have been untraced since 1837. A painting was also mentioned as being on display in Dundee at a musical event in 1872. What we do have is a lithograph, or a reproduction of a lithograph, that may or may not have been based upon the painting by Syme.
Meanwhile, the Oxford Dictionary of National Biography has the drawing above, attributed to John Kay (1742-1826), as a likeness of Nathaniel. What do you think? Kay and Gow were certainly have been around Edinburgh at the same time and I like to imagine that Kay, as a barber, might have prepared his tie wig on occasion, hence the attention to that detail in the drawing.