Final answer:
Option (c) 'My dog has his own bed. He sleeps on the couch when no one is looking, though.' is the correct revision of the run-on sentence, as it separates the two independent clauses with a period, avoiding a comma splice and improper capitalization.
Step-by-step explanation:
Among the provided options, the revision that corrects the run-on sentence "My dog has his own bed he sleeps on the couch when no one is looking, though." in a grammatically correct way is option (c): My dog has his own bed. He sleeps on the couch when no one is looking, though. This revision corrects the run-on by separating the two independent clauses with a period. This makes the sentence clearer and easier to read. Additionally, it adheres to grammatical rules by not using a comma, which would result in a comma splice, and also does not improperly capitalize the word "He" as seen in option (d).