He was illegitimate and he was born prior to the start of civil registration. According to later censuses he states that he was born in Coshieville. It's in Perthshire, still exists today.
Yes; Coshieville is a couple of houses in the parish of Dull. One was and maybe still is the Coshieville Hotel. See
http://www.geograph.org.uk/photo/2967755there is no mention of a William Watson born Coshieville in the 1861 census. So he was missed, not uncommon.
The census is supposed to list the parish of birth, so he should be listed asa born in Dull, not in Coshieville.
Have you looked for William Gilmour, born in Dull, in the 1861 census?
Interestingly, on his marriage certificate of 1878 he states his mother is Margaret Gilmour.
What, exactly, does he say her name is? If she was this Margaret Watson who married Henry Gilmour after William was born, she should be named as "Margaret Watson, subsequently married to Henry Gilmour". If she is plain "Margaret Gilmour" that should indicate that her maiden surname was Gilmour.
Was William's mother deceased at the date of his marriage? If so, she can't be the one who was married to Henry Gilmour, because she is the 42-year-old wife of Henry Gilmour who was born in Dunkeld and living in Monikie in 1881? It's 24 miles from Dunkeld to Coshieville - that's the best part of a day's walking.
On the other hand, I see that William was in Murroes in 1881, and Murroes is near Monikie.
Have you got William in the 1871 census?
If Margaret is William's mother one real problem is her age, she would have been under 16years old when she was pregnant with William. Possible.
Possible, but very much less common than it is now. On the other hand, Margaret's age could be a few years out in the census.
Do I accept that Margaret Gilmour nee Watson is my ggrandfathers mother?
No. You don't have nearly enough evidence to be sure of that. You can keep it in your notes as a possibility while you continue to investigate.
You need to get someone to take a look on your behalf at the Kirk Session records of Dull, and perhaps also Fortingall, just in case Margaret walked the couple of hundred yards into Dull from Fortingall to give birth. The KS records might tell you a bit more about William's father and Margaret.