He specifically stated gun deaths are acceptable as long as the 2nd Amendment is upheld, and not to mourn or show empathy towards victims.
Let us honor his request and stop talking about him. 
Could you cite that reference for me. I’ve never heard it.
'I think it’s worth to have a cost of, unfortunately, some gun deaths every single year so that we can have the second amendment to protect our other God-given rights. That is a prudent deal. It is rational.'
 – Event organized by TPUSA Faith, the religious arm of Kirk’s conservative group Turning Point USA, on 5 April 2023
'I can't stand the word empathy, actually. I think empathy is a made -up, new age term that — it does a lot of damage.'
You forgot a few words and context in the quotes. 
1st Quote:
“Yeah, it's a great question. Thank you. So, I'm a big Second Amendment fan but I think most politicians are cowards when it comes to defending why we have a Second Amendment. This is why I would not be a good politician, or maybe I would, I don't know, because I actually speak my mind.
The Second Amendment is not about hunting. I love hunting. The Second Amendment is not even about personal defense. That is important. The Second Amendment is there, God forbid, so that you can defend yourself against a tyrannical government. And if that talk scares you — "wow, that's radical, Charlie, I don't know about that" — well then, you have not really read any of the literature of our Founding Fathers. Number two, you've not read any 20th-century history. You're just living in Narnia. By the way, if you're actually living in Narnia, you would be wiser than wherever you're living, because C.S. Lewis was really smart. So I don't know what alternative universe you're living in. You just don't want to face reality that governments tend to get tyrannical and that if people need an ability to protect themselves and their communities and their families.
Now, we must also be real. We must be honest with the population. Having an armed citizenry comes with a price, and that is part of liberty. Driving comes with a price. 50,000, 50,000, 50,000 people die on the road every year. That's a price. You get rid of driving, you'd have 50,000 less auto fatalities. But we have decided that the benefit of driving — speed, accessibility, mobility, having products, services — is worth the cost of 50,000 people dying on the road. So we need to be very clear that you're not going to get gun deaths to zero. It will not happen. You could significantly reduce them through having more fathers in the home, by having more armed guards in front of schools. We should have a honest and clear reductionist view of gun violence, but we should not have a utopian one.
You will never live in a society when you have an armed citizenry and you won't have a single gun death. That is nonsense. It's drivel. But I am, I, I — I think it's worth it. I think it's worth to have a cost of, unfortunately, some gun deaths every single year so that we can have the Second Amendment to protect our other God-given rights. That is a prudent deal. It is rational. Nobody talks like this. They live in a complete alternate universe.
So then, how do you reduce? Very simple. People say, oh, Charlie, how do you stop school shootings? I don't know. How did we stop shootings at baseball games? Because we have armed guards outside of baseball games. That's why. How did we stop all the shootings at airports? We have armed guards outside of airports. How do we stop all the shootings at banks? We have armed guards outside of banks. How did we stop all the shootings at gun shows? Notice there's not a lot of mass shootings at gun shows, there's all these guns. Because everyone's armed. If our money and our sporting events and our airplanes have armed guards, why don't our children?”
2nd Quote:
On the quote about empathy, he is talking about Bill Clinton's politics in the 90's leaning heavily on the two words. He never says anything about not mourning or showing empathy towards shooting victims. Would love to see a reference on that one if you have it.
"Bill Clinton in the 1990s, it was all about empathy and sympathy. I can’t stand the word empathy, actually. I think empathy is a made-up new age term that does a lot of damage, but it is very effective when it comes to politics. Sympathy, I prefer more than empathy. That’s a separate topic for a different time.”
Empathy: 
The ability to understand another person's experience from their perspective. 
Kirk seemed to view this as excessively emotional and politically manipulative.
Sympathy: 
A feeling of care and concern for another person's suffering. 
Kirk viewed sympathy as less prone to political misuse.