k.. Power surge really sounds like a bad or defective bulb..
1. Check the plug on the brake lamp replaced. If dirty, clean with electric spray cleaner.
Then compare the new bulb with the exact one on the opposite side rear brake bulb. If different, purchase the correct bulb.
Next, install the bulbs on opposite sides. If this blows a fuse, your new bulb is bad. Purchase new bulbs.
2. I would next try the brake pedal switch. When they go bad or harness is loose, you can get these types of dash symptoms too. But normally a bad bulb causes this..
3. If the problem still exists, check all the bulbs on the side of the car where the original bulb burned out... Another bulb on that side is probably the culprit.. Check & replace all front & rear bulbs on that side: parking light bulbs, side marker bulbs and rear bulbs. Especially replace any bulb found that is wet or rusty.
Turning switch could cause this but the symptoms dont match. Turning switch dont cause acceleration power surges.
The bad emergency switch will normally blow the fuse immediately upon activation. So, Im thinking its not causing this.
Power surges is normally caused by a bulb with wrong voltage/amp, cross wired bulb (where bulb glass is twisted loose from metal base and wires are touching), loose bulb not seated properly with the little knobs locked, or rust/mosture grounding out the bulb. Also remove the rear lamp harness and check for moisture or rust...
I usually replace all bulbs whenever this happens.. Good luck finding this electrical gremlin..