Create the basic neon object. Make it big, e.g. 1024 pixels say
Create say 3 additional layers under it.
Copy the object and paste it onto each layer
On the layer underneath set the object to be the bright glow colour you want. Also make the object on that layer slightly thicker using:
Object > Offset Path. Give it an Offset of say 1 mm, Joins: Round, and a Miter Limit of 4
On the next layer below make is say 2pixels thicker and set the colout to a bit darker.
Same for the next layer.
Then on a new final bottom layer, bopy the first glow layer and use Effect > Stylise > Outer Glow.
Another effect you might want to play with is Effect > Photoshop > Blur > Gausian blur