I went at around 4pm in April and it was in good sunlight. The only issue you might have is students from nearby schools use it for projects so you may not get the photos you want. Each of the two different times I visited, there were people filming. Once it was a movie for a film class and the other it was photos for a photography class.

It's been about a year since I've been there so I'm not totally clear on the details of the hike. I'm also not sure exactly what wheelchair accessible is. From a legal requirements I don't think so. However, the cave is accessible by a fire road which is not paved but was solid enough that I think a wheel chair might make it. The problem is getting to the fire road from the parking lot I believe you have to scamper up a little hill. The fire road does continue down to the main road but I believe there is a gate that might be hard to pass in a wheel chair. My guess is that if we are talking about a motorized wheel chair probably not but if a person is pushing and can maneuver a little and maybe having another person to help it might be possible. If you are in the area my suggestion would be to have someone drive up and scope it out a little. If you look on google maps in satellite 3D mode you can see the issues.