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Watching the Home Shopping Network late one evening,
Clarence saw handheld televisions advertised for only $49.99, so
he bought ten of them, in his lifetime, Clarence was certain that he would
need them all.
The comma between evening and Clarence is correct. Watching the Home Shopping Network late one evening is a present participle phrase, so it must be attached to a main clause. Clarence saw handheld televisions ... begins the necessary main clause.
When a present participle phrase introduces a main clause, you need a comma between them.