I have continued to research the "caisson" topic, and keep finding reference to both the "caisson method" and the "caisson" as a structure (even within descriptions of the method).
The following definition, really says it all...
"caisson: in engineering, boxlike structure used in construction work underwater or as a foundation. It is usually rectangular or circular in plan and may be tens of metres in diameter." http://208.154.71.60/bcom/eb/article/3/0,5716,18863+1+18575,00.html
This definition refers to the structure and then states its uses as both for underwater construction and as a foundation.
In my opinion, I would find it hard to believe that this type of structure was devised specifically for the method of building a lighthouse out in the water. Caisson structures have been used in all different types of construction, and I have found no evidence to suggest that referring to the hollow cylinder structure or box used for the caisson method (or other foundation purposes) as a caisson is a new industry term. The name of the method does not refer the name of inventor of the method, which is very often the case.
http://www.comptons.com/encyclopedia/ARTICLES/0025/00321792_A.html So, I am still unsettled on the topic. It's kind of like asking, "which came first, the chicken or the egg?"
Perhaps the real problem lies in calling a lighthouse simply a "caisson lighthouse"...because there are obviously lighthouses that have been built by the caisson method which utilizes caissons...and then there are lighthouses that sit on caisson foundations that have not been sunk to the ocean floor. It seems a common enough problem that if people see a "caisson" as part of the foundation, they refer to the lighthouse as a "caisson lighthouse", a phrase that really doesn't make any differentiation between the method or the structure. I do agree that if you specifically are referring to the method of construction that the "caisson method" of building a lighthouse is as Dave has described. However, in my opinion, referring to any lighthouse utilizing a caisson as part of its foundation as simply a "caisson lighthouse" cannot be incorrect because the term is too vague.
If I find anything else, I will keep you posted.