Hi, Richard a CR 2032 3V Battery will also do this job very well. Mine is working since August last year.
Polarity you can find out very easy. There is no resistor necessary
If LED is burning its ok , if not change polarity. No fear LED will not die.
All connections should be near by the controller on the right side, i think.
Here you can find the circuits of the Mega STEhttps://www.atariworld.org/schaltplaene/
Mega STE 4 MB / TOS 2.06 / FPU 68881 / Sony MPF 920 Floppy / GigaFile / Eiffel 1.10 / NEC MultiSync LCD 1970GX / PEACOCK Tastatur / CHERRY Maus M5400 / PARCP USB 421 / Mustek 105 Homescan / SM 124 / Lasermaus / QuickjoyTopStar / KAWAI MS720 / Junior Prommer V2.41 / Mega ST Tastatur / Blitz Floppy + Gotek / MCSWITCH / GABI