To mount the neons, just drill two holes in the top of the plastic panels, and mount them there. You might want to try and get a bolt or two that attaches to the frame as well, and not just the plastic. You should also consider weight. The plastic "screws" or whatever they are called that hold the plastic panel to the side of the explorer are strong, but not too strong. So your best bet is to drill some holes through the metal as well so you have a nice solid/strong mounting point.
Another way would be to make some clips/hooks that simply go over the top part of the plastic panel and then attach to the neons. Depends how permanent you want these neons to be mounted =)
Incase you have to mount an inverter as well (I'd assume so w/ the 48 in. neons?) here is how I did it... sorry for the bad pictures, the camera I used was bad and I didn't realize it till after I had already loaded in the film.
I took out the stock sub/amp that was there to make room. It is actually pretty big behind there. You can run the wire from the battery through the grommet near the gas pedal, under the plastic floor piece (piece near the door), and then under the rear seats.
This is just another shot, because I was installing sound proofing at the time, so before/after shot.... You can see the red power cable dangling there.
This is probably the most important for you... I got a 1/2 in peice of wood, made a carboard design for it so it was flat against the wheel well and then got it cut to fit. You see my amp mounted there, but on the other side of the board is the power inverter. The board mounts in pretty easily, because there were mount points for the stock sub/amp, as well as many other misc. holes.
All put back together, you can't see anything except the small wire that comes up from the carpet to the sub. The amp can breathe through the screen for what used to be the stock sub location. I didn't take pictures, but I drilled two holes in the board and put fans (I used computer fans, which can hook up directly to your battery, attached to the switch I use to turn on the inverter) there so that the power inverter would also have enough cooling.
With the cargo cover on... You'd never know there were subs back there =) Cargo net doesn't really do much I dont think... but just for a piece of mind that the subs wont move around, seeing as how they arn't bolted down. Since the amp is hidden, and not mounted to the back seats (check out Carlton's ex for an example) - It is very easy to take my subs out and have a completely empty cargo area. With my amp and inverter perfectly safe.
To run wires to your neons, just run the cord up where the seatbelt mount is. You'll have to figure out how to have switches. The switch on my power inverter simply provided power to an internal relay, so I just have another switch up front that gives power to the relay inside the inverter - bypassing the inverter's on/off button.
I wish I had better pictures, I'll get some one of these days =P