Yes, it's the shift light which draws a lot of current.
As you say you can get a LED replacement or upgrade the power supply which a bigger one. I would try with a 12V 2A power supply for a start.
I get the 12V from the PC power supply, I connect to one of the plugs that usually connect to the hard drive.
Anyway on Ebay you should be able to find different type of 12V power supply.
Double check the polarity is right when you connect it to the rev burner (don't sawp 12v with ground). you can check here if you are not sure.
Cristiano