Ethos (Credibility), or ethical appeal, means convincing by the character of the author.
Pathos (Emotional) means persuading by appealing to the reader's emotions.
Logos (Logical) means persuading by the use of reasoning.
In the letter, I could see a lot of reasoning used, and it also brought up a little bit of the author's character.
Firstly, in paragraph 1, "As a concerned parent who lost a child to a gun accident...", this brought out the fact that he is one who is very concerned about the safety of others. In paragraph 7, " If we continue making it so easy, our nation will continue to have gun-related domestic fatalities...", this statement also brought out his concern for the society.
Also in the letter, reasonings could be found form paragraph 2 to 5. In those paragraphs, Mr Simmons brought up a lot of information to support his point. Among those information, he also brought up a lot points to help Mr Simmons in his fight for stricter gun control legislations. These points he brought up brings up a lot of reason for stricter gun control legislations, which supports my point that in the letter, logos appears a lot of times.
Unfortunately, I am unable to find any pathos in the letter.