tinanam0102“1. He stood at the entrance of Sogo waiting for his girlfriend.”
-- He stood at the entrance.
-- What was he doing at the time?
-- He was waiting for his girlfriend.
His waiting for his girlfriend was an activity that was happening all the while he stood at the entrance of Sogo. In fact, you could even say that his waiting was his standing there.
tinanam0102“2. Jackson's bought ATV in 1985 for about $47.5 million and sold it to Song for about $95 million in 1995, retaining a half interest.”
-- Jackson's bought ATV and then sold it.
-- What were they doing at the time?
-- They were retaining a half interest. [ ??? ]
The second case makes no sense because "retaining a half interest" is not an activity that was going on during the time they bought and sold ATV. Retaining a half interest is another separate action that happened.
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Take these examples for further thought.
They all had an amusing evening telling jokes.
What were they doing at the time they were having an amusing evening? They were telling jokes. The activity of telling jokes was going on at the time they were having an amusing evening. In fact, you could even say that their telling jokes was their having an amusing evening.
The man eventually left, taking his dog with him.
What was he doing when he left? He was taking his dog with him. [ ??? ]
Taking the dog was not an activity that was going on all the while the man was leaving. It was a separate action (or event) that happened when the man left.
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To summarize:
Did he stand at the entrance and wait for his girlfriend as separate activities?
No. His standing there and his waiting are in fact the same situation.
Did they have an amusing evening and tell jokes as separate activities?
No. Their having an amusing evening and their telling jokes are in fact the same situation.
Did the purchase and sale of ATV occur separately from retaining a half interest?
Yes. The retention of a half interest was another, though related, event.
Did the man take his dog separately from leaving?
Yes. Taking the dog was another, though related, event.
CJ