How to repair (or find someone to repair) a Neon Light?

Find a sign company near youo that deals in neon.

It won't be cheap unless the problem is very simple,

such as a bad power switch.

Cost could be anything from $25 or so to $350, or maybe even more.

Check its high voltage power source ( more than 5000V ) that attached on both neon tube ends to see the power source is working. Next check the link wire between tubes and make sure no broken wire.

* No shop offers to repair this out of dated old product. Neon gas in tube can be all burnt out or leak through its small filling hole (glass pig tail ), Refill it requires a special service shop that charge a lot of money.

Neon tubes are just specialised fluorescent tubes. 

So just like those, they have a finite lifespan and when they finally die they should just be scrap like normal fluorescent tubes.

But they’re not. Neon tube makers can use the glass envelope to make a new tube; it makes sense because the specially shaped glass envelope is the most expensive and labour intensive part to re-make from scratch.

A neon tube manufacturer can cut off the ends which hold the worn-out electrodes, clean out the tube fluorescent coatings and replace them if necessary, and then use a blowtorch to fit new electrodes set into glass to the cut ends of the tube. It then gets put onto a vacuum pump before being refilled with neon and a tiny bead of mercury.

So no, it cannot be repaired but the main expensive part can be used to remanufacture the tube to be as good as new.