The first version is correct. The second version does not exist.
It's like I must have / had forgotten to lock the door.
You could switch from present perfect to past perfect in this way: I have been the shadow of your shadow, because I have / had thought it might keep me by your side.
Using "had" would mean the thinking preceded the acting.
"Have been" is present perfect; "thought" is simple past. You could bring the thinking up to past perfect continuous (had been thinking) or present perfect continuous (have been thinking).