For the next artist I only found an engraving, not a self portrait. There will probably some more artists to come without a self portrait. We’ll see…

Francis Cotes
(1726 - 1770)
 

Francis Cotes RA was an English portrait painter, one of the pioneers of English pastel painting (or drawing), and a founding member of the Royal Academy in 1768.

https://en.wikipedia.org/wiki/Francis_Cotes

Portrait of Francis Cotes RA, 1792?
After Pierre-Étienne Falconet (1741 - 1791)  

Peter (Pierre-Etienne) Falconet was a French portrait painter. This is his self portrait:

And this was the portrait posted in July by Francis Cotes:

Portrait of Joseph (1741-1786) and his Brother John Gulston (1750-1764)
Posted on July the 7th.