Need advice @ stray

We camp host and will only be at our present site for 6 months. A cat approached us the first night we pulled in. Friendly, extremly anxious, meowing, needy, very thin but not emaciated. He isn't neutered and no collor. He willingly came inside. He ate fast as if he hadn't eaten in a week. For about one hour he kept getting up for more food and drank a lot of water. He was extremely anxious and on edge, talking and jumping at every sound. He meowed and followed us everywhere we went almost in a panick. He finally fell asleep on our bed. He woke up often all throughout the night to get love, lay on our chest/laps and eat more food. At sun up he wanted out. He left and didn't come back until sundown. The second night he was totally different. At sunset, He meowed at the door. He came in and allowed us to pet him. He layed down for 30 minutes and then wanted out. He wanted in and out and in and out and
finally left. He came the following morning for a quick bite and left until sunset. Tonight. Same. He ate and went outside and layed in a chair for about one hour and left for the night. Tonight he is calm, and no longer anxious. He didn't want in and out. He seemed settled and more confident. My question is: How do I know if he has a home that he disappears to each night? Should we adopt him? Take him to the vet for vaccine and neutered? Take him with us when we leave in six months? He seemed very lost, thin and hungry the first night. But now I'm doughting my instincts. This state park has many strays. I don't want to leave him behind, but I also don't want to take him from his home. Suggestions?

 

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What type of advice you want

 

Should I keep him?