Is my cat ill or grieving?

We rescued Beckham in off the streets about four years ago. He was never 100% confident around us, he seemed skittish when we showed him affection but he loves a good chin scratch and belly rub and often let's us stroke his back. But lately when we go to stroke him he moves his head back or to the sides and if we go to stroke his back, he dips down, this behaviour comes and goes, one minute he'll let us stroke him etc, the next he moves away. He has been acting strange, lying in places he doesn't normally lie and acting up. But my niebour told me today that his cat died a couple of weeks ago, around the time my cat started acting strange. My cat is an outdoors cat and we often see him roaming around my niebours house and starting fights with his cat. His cat was a female at 19 years old and my cat is a male at 12 years old. Is it possible for cats to feel emotional about the loss of another cat like we would with one another. I'm wondering is my cat showing signs of illness or grieving?

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