My Male cat won't let me get near him or touch him

Hi, 2 years ago my neighbors moved and abandoned a pair of 1 yr old siamese (male and female. Saw them hungry and lonely so i bought them food and adopted them. I've never had cats. My mom doesn't like cats so they don't live inside the house. Soon after i started feeding them, the female cat bonded with me, she sneaks in the house when i'm inside to look for me, makes me company and even sneaks at night ands sleeps in my bed with me, when i'm not in the house, she doesn't even set foot in the backyard.

What i wanted to consult with you is that the male cat, even after 2 years, just won't let anyone get near him. Only I can get about 10 inches close to him if i don't make eye contact (he stays 2 feet distance from everyone else, he always acts scared around people never aggressive not even when I try to touch him, he just jumps away). I even bought him a bed because he sleeps outside and he won't even sleep on it, he sleeps hidden somewhere.

I wanted to know if there is something i can do, or if he's just traumatized and is never going to get close. My worry is that if he gets sick or something how am i going to help him? They are both spayed an neutered (i assume because in 2 years i haven't seen one single siamese kitty around) or eventually i would like to take them both to the vet. thanks in advance for the feedback.