Neon would probably be more common, because all the bulb requires is a series resistor (perhaps 220k, but value needs to be properly calculated for your application). If the bulb emits a lovely orange glow, then it's almost certainly a neon (such as the famous NE-2).
LEDs are posssible, but they require slightly more elaborate power supply (series capacitor, which are probably too large and bring safety requirements). I don't recall ever seeing LEDs used in the application you describe (molded into the cord).
Never seen anything BUT neons in that application. Same as power strip power switches.
Notable is that as the neon is lost over time thru leaks or thru being trapped by metal ions against the glass the glow will get dimmer and dimmer until it starts flickering like a candle. When it gets that way in a dimly lit location you will note that it will glow solidly if more ambient light lands on it. The extra photons impinging on the metal rods causes more electrons to leap off increasing the bulb's current via the Work Function.
Heinrich Hertz discovered this phenomenon in late 1800s but Einstein actually wrote it down as the Photoelectric Effect winning the Nobel prize for it in the 1920s. The Photoelectric Effect is what led to light being understood as having quantized packet-like behavior.
It's a subject dear to my heart. As a college student I was hired and paid (amazingly) to build a Work Function Demonstrator for the physics department.
I wondered when a power strip in a cabinet flickered but when I opened the cabinet door a little more to snake my hand in and turn the strip on the neon indicator always instantly glowed normally.