ANSWER: It's unfortunate that many people equate sex with love. Such people are the ones who promote the idea of David and Jonathan being gay.
Now comes a problem. These same people have an ally in the Hebrew language. The Hebrew word for love, ahab, (Strong's Concordance of the Bible, #H157) in 1Samuel 18:1, 3, and 20:17 refers to having affection for someone either sexually or otherwise. Naturally those who see David and Jonathan as gay conveniently overlook the OTHERWISE.
They also overlook the fact that ahab is used elsewhere in the Old Testament for non-sexual love. In Genesis 22:2 God told Abraham to offer his son Isaac, whom he loved [ahab], as a sacrifice. With Abraham more than a hundred years of age, and Isaac being a young adult, this was not some gay sexual love. Isaac was old and blind when he called for his son, Esau, to shoot a deer and "make me savory meat, such as I love [ahab] " (Genesis 27:1-4). Certainly nothing sexual in this.
Possibly the most important consideration of the word LOVE is in the Ten Commandments (Exodus 20:4-6, Deuteronomy 5:8-10). In speaking to the Israelites, God said, ". . . you shall love [ahab] your neighbor as yourself." (Leviticus 19:18). If this sounds familiar it's because Jesus said the same thing in Matthew 5:43 and other New Testament scriptures. The Greek in these scriptures is Agape (Strong's #G25) referring to loving in a social sense, or having benevolence toward a person.
You are right in saying that even if David and Jonathan's relationship was not sexual in nature that nevertheless their connection must have been intimate and their separation deep sadness. When you have lived seventy years you will have experienced the pain of a loved one leaving. But, even then, it really won't be as distressful as their parting. They couldn't pick up a telephone and contact each other, as we can, or even send an Email. We can travel farther in a day to visit our friends than they could in weeks. Only through death might our parting be as distressful as David's was.
In conclusion, King David was not gay and neither was Jonathan. What they had between them was a deep friendship and nothing more.