said by ArgMeMatey: said by Gemstone:
The control transformer is part of the oil burner (Riello)... It is marked as 24VAC output... Only has 2 terminals... I measure 32VAC across the terminals...
In that case, you might also check a site like heatinghelp.com.
There are probably a million Riello oil burners with identical transformers and all kinds of Honeywell stats, so chances are somebody there has already scratched this itch on their own head.
Best to you.