Do you think the following bit of text is grammatically correct ?

The Shop

He went to the shop to buy some food. When he got there the shop was closed. He went to another one, which was closed too. There were just 3 shops in the neighborhood, and he knew that if that one would be closed, then it would leave him no other option but to spend the night hungry. He knew the chances the last shop would be open were slim. Yet he went on to try his luck.
He saw the light in the building was on as he was approaching. The closed sign on the door hadn't been put either, so evidently the shop was open. "Lucky this time" he thought. He pushed the door and stepped in.

Thanks!

Question

Do you think the following bit of text is grammatically correct ?

The Shop

He went to the shop to buy some food. When he got there the shop was closed. He went to another one, which was closed too. There were just 3 shops in the neighborhood, and he knew that if that one would be closed, then it would leave him no other option but to spend the night hungry. He knew the chances the last shop would be open were slim. Yet he went on to try his luck.
    He saw the light in the building was on as he was approaching. The closed sign on the door hadn't been put either, so evidently the shop was open. "Lucky this time" he thought. He pushed the door and stepped in.

Thanks!

Answer

I would also change the part about the closed sign.

The open sign on the door hadn't been turned around either,... (Some shops traditionally have a sign with open on one side and closed on the other)

The closed sign on the door hadn't been lit up either,

It depends on the closed sign, 'put' either needs to be 'put up' or 'put round' or changed to another word.

Answer

I’d change it to ‘if the last one was closed’ but otherwise - very good :)