In Full Metal Panic, why does Sousuke call Hayashimizu Atsunobu "Your Excellency"?

Question

In Full Metal Panic! Fumoffu?, we see Hayashimizu Atsunobu, the Student Council President. When Sousuke addresses him, he always calls him "Your Excellency" and stands at attention.

He seems totally fine condoning Sousuke interrogating the thug who passed on the message that Chidori had been kidnapped (closing the blinds and not stopping Ren or Sousuke).

While in a school environment, he is a figure of authority, but he is hardly the highest authority with the teacher still above him, and Sousuke never uses similar terms for any teacher.

So why does Sousuke call Hayashimizu Atsunobu "Your Excellency"?

Answer 1

Hayashimizu's shall we say "extraordinary" tolerance for Sousuke's school shenanigans is a separate question, so I will abstain from that and focus on your primary issue:

The short answer is: it's a joke, based on Sousuke's inability to distinguish between the nature of life in the school environment and life in the dangerous geo-politico-military environment in which he's lived his entire life. Hayashimizu is introduced to him as the school's President. In real life, nobody is higher than a President (certainly not any "mere" Teachers!), and so he defers to him accordingly, as if he were the President of an actual country. "Your Excellency" is a formal way to address a President, or any Head of State. The humor comes from Sousuke's exaggerated politeness and formality whenever dealing with somebody who is in reality merely another student, with some extra after-hours responsibilities!

(However, it should be noted that in the light novel, "Continuing on My Own", their conversations show that both have developed a very real and deep respect for the other, based on their history and knowledge of each other's personalities.)