Mark,
Your mind works like that too then?
As to your question, I would say that he may have actually known the number of ships present at the battle before it commenced. This is off the top of my head, but I would imagine that a day or so before the battle the number, and names, of the ships at Trafalgar would have been known by almost all the ships in the Fleet, certainly by the captain and officers, if not the ordinary seamen – and news travels fast.
Being part of the signal's staff, Eaton would surely have been aware of each ship 'making her number' to the flagship as she arrived and I would imagine that other ships were also keen to read the signals to know who was in the 'team'! I seem to remember Nelson also gave direction that the order of sailing was the order of battle, and seeing that Temeraire was next in line astern of the Victory, Eaton must have had a relatively easy task in reading all the signals made to the flagship.
I'm not saying, of course, that Eaton didn't use other sources for verification, and it is probably likely that a lot of his log entries were written subsequently, but I feel confidant that the number and names of the ships present would have been more or less immediately known.
I may be wrong of course, but that's my opinion!
