The ignition wire is only used for signaling to the empeg (much like the remote wire to the amp), power is drawn on the permanent line (at least for the MkIIa, the MkII, IIRC could pull power from the ignition wire as well...)

Does it dim whenever you let the RPMs drop, even if you're not brakeing?
If no - look at ground points. The current through/from the brake light might be raising the voltage at a [bad/corroded] ground point so that things get confused (charging regulator etc) Any similar effect if you turn on/off other heavy consumers like fan or rear de-mister?

If yes; sounds like your battery is far from full and/or your alternator is struggling...

I'd check the battery further - being drained completely is bad for starter batteries, especially if they're a couple of years old.

Measure the density of the acid in each cell; it may not show full charge yet (1.28 - 1.30 g/cm^3) but should at least be consistent across all 6 cells. If one cell is significantly different you battery may be broken. Take it to a shop for a load test (draw heavy current from it while monitoring voltage - you should be able to draw the CCA rated current for about 10 seconds without the voltage dipping below 9V (if the battery otherwise is reasonably charged). If it does dip, look down into the "odd" cell (glasses recommended!) - odds are good that you'll see it bubbling/boiling (a lot more than the others) - replace battery.

Also check you alternator: should at least give a bit more voltage than pure battery voltage when car is idling; increase RPMs to about 2000, voltage across battery should rise to at least 13.8V, but not over 14.4V. If not, most likely your charging regulator needs replacement. On most modern alternators it is combined in a unit with the graphite brushes (the reg might be OK, but the brushes worn out - should give low voltages)

/Michael