Using  Neon Flex and LED Tape.
Most El Wire is not bright enough to be easily seen in daylight so is not suitable for Neon Signs.

Neon signs are made from glass tubes with the inside coated with a phosphorescent powder coating. Different coloured sections of glass tube can be joined together to produce different coloured sections as shown in the picture. The glass tube is filled with a purified argon gas mixture and the gas ionized by a high voltage between the ends of the tube with electrodes. Neon gas can be used in a clear glass tube and has a yellowish orange colour. The “hidden” sections are black.
https://en.wikipedia.org/wiki/Neon_sign

Neon signs became expensive due to environmental restrictions but are still in use with many heritage projects keeping the craft going. Alternative materials such as El Wire, Neon Flex and LED Tape are cheaper and easier to use, but do not have the brightness of Neon. These cheaper alternatives still require artistic craftmanship.

This Comparison of Various Light Sources Output Efficiency, Color Range, & Lifespan does not compare Light Output  http://www.neonshop.com/Tech/compare.html

Neon Lighting states Lumen output from neon tubes is 500 lumens per foot. Neon Tubes generally come with four (4) sizes in diameter 9mm, 10mm, 12mm and 15mm. Any size above 15mm are called Cold Cathode Tubes . http://neon-lighting.com/neon.htm#:~:text=Lumen%20output%20from%20neon%20tubes%20is%20500%20lumens%20per%20foot.&text=and%2015mm.,are%20called%20Cold%20Cathode%20tubes.

Neon Design has a Light Output Chart for Neon Sign Tubing http://neondesign.com/technical-information/light-output-chart/

The Grindhouse sign appears to be made from Neon Flex LED strip lighting. In the close up picture you can see how the long straight parts of the “d” and “h” are not joined on to the other sections of the letters, there are end caps on the sections of Neon Flex and the connecting 12V wire can be seen. One small section of the “o” has faulty LED’s and is not illuminated.

To see a Neon sign, look at the end of building 3 on the way to Cafe 10.

I have put this project above the El Wire section due to the El Wire being very DIM ! 
Caution, do not use MDF the dust is deadly.

How to Make a Realistic Faux Neon Sign – Super Bright! https://www.instructables.com/id/Realistic-LED-Neon-Sign-Super-Bright/

LED NEON ART SIGN Making https://www.youtube.com/watch?v=oeKtM4JJpBw
The youtube video shows how to make seperate letters and connect them together to make a circuit.
The NEON Flex does not look this bright during construction, the finished image is in a darkened environment.

Getting Started with Electroluminescent (El) Wire    https://learn.sparkfun.com/tutorials/getting-started-with-electroluminescent-el-wire/all
Excellent overal guide on different shapes, sizes. Lots of how to videos, links.

Soldering to El Wire   https://learn.adafruit.com/el-wire/soldering-to-el-wire
Lots of pictures showing you how to solder and join El Wire. Caution El Wire uses at least 100V AC low current so it has to be insulated.

 

Little Bird Electronics sell a range of El Wire  https://www.littlebird.com.au/search?query=EL%20wire  that has a 3V to high voltage inverter. Quicker supply times than overseas suppliers. One sample ordered is 5M Flexible el wire with battery holder 5mm – Orange.  https://www.littlebird.com.au/products/5m-flexible-el-wire-with-battery-holder-5mm-orange 

Mounting El Wire or Neon Flex
Some of the options are:
Thin clear perspex panel.
Thin opaque or white perspex panel.
Thin perspex sheet so you can edge light it using LED’s or LED Tape.
Backlit box with white perspex front using LED Tape.

How to Make a Realistic Faux Neon Sign   https://www.instructables.com/id/Realistic-LED-Neon-Sign-Super-Bright/
Different aproach, he backlights the clear plastic tubing used to make the letters, but construction ideas here.

I have put 3 samples of Opal plastic in the workshop. You can see that the 3mm Opal 010 acrylic is almost transparent which may suit the Central Perk sign, the 4.5mm Opal acrylic is translucent so may suit the Neon Flex sign.
The samples came from The Plastic Display People 4/50 Howe Street, Osborne Park W.A. 6017 phone 94442270.
Note that white plastic is not transparent.

There is also a piece of 1mm and 2 pieces of 6mm pespex that are secondhand.

page updated 17 August 2020