You really believe that was just your second thought on this topic?
It’s not that simple: First thought. Second thought. Third thought.
It’s not that linear: One thought that triggers the fall of other thoughts like in an assembly line of dominos.
A more accurate statement is to say “after further contemplation…” because your thoughts are spontaneous, deliberate, causal, and iterative.
This is good news. You have more than two thoughts on any given topic… you have more than two shots in any given endeavor… you have more than two choices in any given proposition.
The phrase “on second thought” perpetuates the pitfalls of binary thinking: Always or never. Black or white. Yes or no.
On second thought, you have more than two thoughts…
Perhaps, after you stop counting your thoughts, you will start enhancing your thought process… it is a process after all, so you are bound to eventually lose count.