I found this articulating and lighted inspection mirror with a clip no less in the women's makeup isle at Wal-Mart for less than $10. It comes with a USB to micro usb charging cord.
Lights off for this face
Mirror rotated
Lights on and slightly rotated for underneath/backside of engine mount
Lights off for this face
Mirror rotated
Lights on and slightly rotated for underneath/backside of engine mount