Mathew - the oil for the dashpots should be engine oil or thinner. You may have overfilled a little - it should be about a quarter of an inch below the top of the tube. If there is too much in there just remove the covers - 4 screws- empty out and start again.
A V12 E Type - when properly tuned - will be smooth at tick-over. The usual cause for lumpy tickover will be the carbs not in sync. One,two or three of them will have an idle setting different from the others. There are four idle setting screws - back them off and then screw down equally.
Importantly, between each pair of carbs there is a screw which holds the link between them together. Make sure these screws are just in contact with the link.
If you think that one bank of 6 cylinders is not operating you would certainly know about it! The car would be unlikely to move when in gear and it would tick over like a pig. If this is happening, suspect the twin headed fuel pump - one pump may be failing, thus limiting the supply.
There are no separate electrics to each bank of cylinders (except obviously the plug leads), so if one side is dodgy, it is likely to be a fuel supply problem or, much more likely, a carb set up issue.
Hope this helps.