Dear All About Circuits,
Recently I bought a lamp for my industrial sewing machine which runs on AC Mains power (Rated at either 110V or 220V), for the sake of having the lamp power on when I power on the Sewing machine (and for a bit of fun) I wanted to reconfigure it so that it connected into the outlet on the back of the sewing machine (bottom right picture). I have no education in electronics so through a lot of googling I have got to this point, but am now at a loss.
Below is a circuit diagram of how the light works, I have become stuck trying to measure the forward voltage across each LED light, all my multimeter shows me is the number 1. Instead I have tried to provide as much information as possible, such as measurements taken from across the 30x LEDs says that they are drawing 28V and 0.04A, meaning that they have a resistance of 700 Ohms I think.
I would really appreciate someone telling me if it is possible for me to reconfigure this light so that it can connect it to the 5VDC, 1W, <100ma outlet on the back of my sewing machine and if so any ideas how. Do I need a DC-DC voltage booster? If i did would it even be possible? Argh!!
p.s. my idea if i can't is to wire the lamp and sewing machine into a junction box and then use a relay plugged into the outlet which will power on the LEDs which I'm pretty sure will work!

Thank you for any help what so ever!
Recently I bought a lamp for my industrial sewing machine which runs on AC Mains power (Rated at either 110V or 220V), for the sake of having the lamp power on when I power on the Sewing machine (and for a bit of fun) I wanted to reconfigure it so that it connected into the outlet on the back of the sewing machine (bottom right picture). I have no education in electronics so through a lot of googling I have got to this point, but am now at a loss.
Below is a circuit diagram of how the light works, I have become stuck trying to measure the forward voltage across each LED light, all my multimeter shows me is the number 1. Instead I have tried to provide as much information as possible, such as measurements taken from across the 30x LEDs says that they are drawing 28V and 0.04A, meaning that they have a resistance of 700 Ohms I think.
I would really appreciate someone telling me if it is possible for me to reconfigure this light so that it can connect it to the 5VDC, 1W, <100ma outlet on the back of my sewing machine and if so any ideas how. Do I need a DC-DC voltage booster? If i did would it even be possible? Argh!!
p.s. my idea if i can't is to wire the lamp and sewing machine into a junction box and then use a relay plugged into the outlet which will power on the LEDs which I'm pretty sure will work!

Thank you for any help what so ever!