Another option is...
Find the door wire off the terminal, and run a split cable onto it, and down to the neons as their positive, then earth the neons directly to the chassis near the footwells. Either way, there will be more current going to the circuit, so youll have to put in a bigger fuse.
OR...
You could hook a relay directly to the door switch so when the drivers door opens then the neons come on through a totally seperate circuit which you build from scratch so it doesnt piggyback anything else's fusing.