Mr. Detail--the 3rd light brake only has a single bulb. If the instrument bulb indicator on the dash comes on, it means that either that particular bulb is burned out or, some other bulb is burned out. Obviously this is not your situation, so the next situation applies: you replaced a burned-out bulb on one side of the car and not the other, using two different brands, e.g. Philips vs. Sylvania. The resistance in the hot lead of each bulb is enough, even though it's the specified one, to trigger the instrument bulb light on the dash into coming on because of the resistence differential between different brand bulbs and, sometimes even between a new and worn one of the same brand.

Since the the third brakelight is a single bulb, and not in parallel with another bulb (i.e. two brake or backup lights), I don't know how that particular bulb, if it's good, is triggering your instrument panel light. Even if there were a poor connection, e.g. bad terminals, and, because it is a single bulb, it would not trigger the instrument warning light if it were still working. However, if the base connection were really bad, and it only worked part of the time, yes, that would do it, but the instrument warning light would be intermittent. Dick