I just can't imagine that's the extent of it - no hose length requirements, etc...
You have to remember what the Cavern diver course is - it's an introduction to diving in the overhead environment, with no restrictions and always with in the light zone.
You need three light sources, because you always have visual reference to the outside that means you need to carry two with you. You can kinda work with any torches, but you will find that the type of torch and the type of reel can make life either very easy or very hard.
Because there are no restrictions, it is very easy to do the required air sharing exercises using a normal reg and 40" octi. You will find that most instructors will counsel you about hose length. The skills on the course don't involved blind gas sharing exits - this is the only situation (other than restrictions) that a 40" octi hose will be a limitation. There is just no way of easily maintaining contact with your buddy, and with the line, whilst sharing gas using a standard 40" octi. When we teach Cavern courses we prefer students to have a 7' hose, but will generally provide regs for students to use. The skills on the line circuit are enough to convince someone of the value of a long hose.
The PADI Cavern course is a very well thought out course, with good content and structure that is entirely appropriate for the course goals. But, unfortunately, there was a period of time where instructors were approved to teach it having only done an Intro-to-Cave cert. That has now changed, new instructors have to be fully cave qualified and well "full cave kit" - but none of the old instructor ratings were rescinded. As a result, it is important to shop around and find a good instructor. Look for recommendations - but as a minimum, look for ones who are full cave qualified and cave dive regularly. These may be cavern instructors for other agencies (e.g. NACD) and may encourage you to do those courses instead - their opinions are valid, listen to the pros and cons they present and make an informed choice on the basis of that information. Other people who aren't full cave qualified, or don't teach Cavern courses simply don't have all of the facts. Find people who do.