Can I write the sentence like this?
“I was too busy looking at it during our way down that I forgot to take pictures.”
I don’t think “busy looking”. I think “adjective” should be followed by a “to Verb”
Eg.: I was too tired to say something.
Thanks in advance.
This is my take on your question:
“I was too busy looking at it” is a natural usage.
“I was too busy to look at it” is natural too, but it has the opposite meaning! It means that you were too busy doing something that you didn’t have the time to look at it.
The sentence “I was too busy looking at it during our way down that I forgot to take pictures.” has real problems in other aspects. The examples below would be better:
I was so busy looking at it on our way down that I forgot to take pictures. Or,
I was too busy looking at it on our way down to think of taking pictures.
Be busy doing X = Be busy in doing X.