The oil boilers seem to be a collection of parts not all made by the same manufacturer, and my heatslave is likely not the same as yours.
I did work on oil space heaters in the past, and they were a pain, but the main method was if not sure, change it and see if it works, which is all well and good when one has a store full of spares, and if it proves that was not the cause you can put it back in stock, but not much good when one needs to order parts special.
But it seems the start point is the meter in the flue, and check the burner is running at the correct rate, as other wise the photo cells can be damaged or soot up. I would often pull out the photo cell wipe it, and hey presto running again, I found that the jets wear, so the flame is not correct. I did not have fancy meters on the Falklands so just fitted smaller jets.
Here in the UK I simply found a heating engineer to do it for me, I do not want to be paying over the odds on oil, so DIY is simply not worth while, as I would need to buy special meters, yes over £100 for a full service, but only get it done every other year, did not aim to do that, just the guy never turned up to do it last year.
Year one he must have visited around 3 or 4 times, not here long, and only charged for work done, if he returned for same fault it was FOC, it seemed the main problem was a solenoid, but the unit had not been serviced in years, and the pipe work and controls also up the creak.
If you must DIY I would say a clean is the first thing to do, most faults seem to be caused by soot. But would say getting it set up correct means less soot, and also likely use less oil.
