briggs and stratton 25hp valve cover not heating up evenly

[bertsmobile1]

B & S Coils should not be handed ( Honda coils are ) but if one of them was originally fitted upside down then it would not fire at the correc time ( if at all 0 due to the way that the Hall Effect Trigger works
So both coils should be fitted the same way round with the kill lead tab facing the cylinder .
FWIW
If flipped the induced voltage will be 180 deg out of phase
On B & S magnetron coils the voltage in the coil goes from 0 - peak negative - 0 - peak positive - 0
When the chip sees negative X µV it fires the coil
If the coil is on upside down it goes 0 - peak positive - 0 - peak negative - 0 so the spark will happen ( or try to happen ) just after the magnets have passed the laminations rather than as the magnets are passing the laminations.
So at best you will get a very weak retarded spark or at worst , no spark at all .

 

[Forest#2]

and as bert says they can be installed upside down.
If you look very close and carefully at the black plastic some are labeled in weak small letters, this side up.

You say it surges slightly at mid and upper throttle W/O a load on the engine
If it smooths out under load it will probably be ok.
Might add a fuel additive such as Seafoam to the gas as a carb cleaner.

Sometimes if the rig has a manual choke you can give it just little bitty bit of choke little at a time and correct a light surge due to the carb running little lean and a gas carb cleaner additive might eventually clear such.
In my post #18 you will see tips how I've cleared up a rough running Nikki carb sometimes W/O have to remove the carb by removing the 3 screw top plate.

Sometimes (if all else is correct) a governor static adjust is on the edge of not quite correct, but some of them Intek OHV twins governors do not ADJUST correctly by the book so best to try and live with it as is for now probably. (they can be tricky (trial and error method) to adjust sometimes)