Ron,
The entry in the Royal Military Calendar for Captain Carthew (Vol V p 364) is quite clear that he commanded "the light infantry companies of the brigade".
Similarly the entry for Major Thomas Pearson Vol IV p 340 shows him as commanding the light battalion of the Fusilier Brigade of the 4th Division, and mentions this several times.
These temporary light battalions were of course normally only a half-battalion of 4 or 5 companies, so perhaps that is why their commanders did not receive the medals which a "proper" battalion commander would.
I have just downloaded all 5 volumes of the Royal Military Calendar 1820, which was not easy since most of the volume numbers are shown incorrectly on Google Books, but all five volumes are there. I will now trawl through them looking for other mentions of officers commanding these temporary light battalions. That should keep me busy up to Christmas!!!
Rod