Hi Terry,
Correct me if I'm wrong, but that light appears more or less orange when it's on, doesn't it? If so, that would confirm my belief that we're looking at a neon bulb; they were a favorite of appliance manufacturers for many decades. If you have a voltmeter you can confirm that it's got 120V on either connection, but from your pictures I'm pretty sure of my diagnosis. There may be a resistor connected to the bulb; if there is you'll want to keep it unless the bulb you get comes with one.
You can get them pretty much anywhere; although you can find them cheaper, here's a pretty inexpensive one on Amazon.
[link|https://www.amazon.com/Eiko-A1A-Terminal-Halogen-105-125V/dp/B002CYXHVQ?th=1|Amazon.com: Eiko A1A T-2 Wire Terminal Halogen Bulb, 105-125V/0.6 Amp, Neon : Everything Else]
A search for "110V Neon Bulb" will turn up lots of choices. It looks like you'll need to solder it in or use some wire crimps; I can't see exactly how it's connected to the circuit.
Hopefully that'll get you going!