but I don't know the exact name or gauge but it looks like this
yup thats defo telephone wire
It looks like phone wire,you may have to remove the outer casing. t
A lot of times your local hardware store will have stuff like this that the big boxes don't stock.
It looks like really thin guage electronics wiring. Try Radio Shack.
Try to find thermostat wire. Most do it yourself centers carry this. It is about 18 gage and can be formed and hold the shape better than phone wire which will be a lighter gage and will be stranded wire.