I'd figure it's a corroded battery in the cluster. The CEL gets power directly from the battery, and it's grounded on by the DME to turn it on.
Pull fuse 10 to turn off the CEL, see if your battery drain is solved. The gauge cluster isn't that hard to get out, just a little tedious. Once you get it apart, check the batteries on the SI board for leakage. If they've damaged the board and caused a short, you could see problems like you're having.
There are a few different versions of that board, be sure to get the correct replacement cells. A lot of us (including Froos) have wired up a remote battery. If you're handy with a soldering iron repairs are pretty straightforward. Refurb units are still available from Programa AFAIK.