Running 4 Neons from Cigarette Lighter

I'd be careful doing that.  someone i know hooked up 4 neons to the same cigarette lighter, and they only worked for about 10 seconds and then they went dead.  the lights never worked again.  if you could somehow split it up (like if you have 2 separate cigarette lighters) try doing it that way, but i wouldn't run them all from the same cig lighter.

Ok, so splicing 4 neon tubes into the Cigarette lighter is not a good idea.  I have sketched up something different using a relay switch.  I have attached my rudimentary sketch.  That black box with the numbers 87,85,86,30 is the relay switch.  Can someone take a look at this and gime me your comments and suggestions. What amp fuse should I use?  And more importantly, will this even work?

Ok, I installed my neons as shown in the diagram above but now i have a funny problem.  The first problem is that every now and then, I hear a pop in the rear driver's side speaker.  But this is something I can deal with.  The second, more annoying, problem is that a pair of my neons keeps going out.  Its not the actual neons that die, its the inverter that gets fried.  As you can see in the diagram, I had made a little box to plug all my neons into.  I later found out that each inverter can support two neons, so basically, two of those connections are of no use on the project box.  Anyhow, I checked all 4 sets of connections on the project box with a multimeter and they all were outputting 12v.  I have one wire that goes to an inverter located behind the center console, which then powers the two neons under the front dash.  The other wire , from the project box, goes to an inverter located under the center arm rest, which then powers the pair of neosn under the the driver and passenger seats.  These are the neons that have gone out twice because the inverter got fried.  I opened the inverter up and looked at it...some of the little things that look like transformers were burned or maybe melted.  Does anyone have any idea as to why this would happen only to the neons in the back even though they are powered from the same location??  I can't keep spending money on new neons, I have one more inverter left and I dont wanna use it until i can fix the problem.