A sign that a stranger cat likes you and needs you

Some of us don’t need to go in search of a cat companion at a rescue centre or some other place because they come up to you and may tell you through their actions that they like you and need your support.
The difficult part is recognising the signals and of course you have to be in a position to adopt that cat there and then or very soon afterwards.
This has happened to me. I adopted my late Binnie this way in London. She came up to me and I fed her and took her in. A day later I got cold feet and asked my neighbour if she wanted a cat. At that time I had fed Binnie so copiously that she looked pregnant so my neighbour was put off. The rest is history.
I feel that if a person loves cats they know instinctively when a cat, who they have never met before, shows signs that he is ready and in a position to be adopted.
One such case occurred to a cyclist in the UK. He stopped at the entrance to a tunnel in Bath called the Combe Down Tunnel.
A cat came running up to him from the woods. The cat requested some tummy rubs and then climbed up his arm and settled down on his backpack which he was wearing at the time. She had settled in and at that point you could be forgiven for deciding that she had adopted the cyclist.
Unfortunately the cyclist was not in a position to adopt this stranger cat.
It must surely be a convergence of coincidences whether or not a person adopts a cat under these circumstances. If the person is by coincidence looking for a new cat to adopt then it probably would cross her mind to adopt a cat who came up to her just like this one.
The only other problem, of course, is the obvious one that the cat may well be “owned” by somebody else and I wonder whether that actually matters. Legally it does matter but in a moral and practical sense it might not because it seems to me that if a cat behaves in this manner he’s telling you that he would like to adopt you and live in a new home. Are cats able to have this thought (yes) and communicate this idea and message?
I have a feeling that they do these things through their actions. It just takes a little bit of sensitivity on the part of the person to get the message and the courage to say yes.