OK Bob/John,
Sorry for this long post - and thank you so much for your thoughts and time.
It still shows that 10.0.1.3 wireless client. But now I think it could be my MacBook as the 10.0.1.3 wireless client on the TC has the same hardware address (xx:xx:xx...) as the one that shows in my System Information panel in the Network/Locations folder under the Wi-Fi Hardware (MAC) Address - see screen shots.
Bottom line - 10.0.1.3 could be my MacBook, but is it really - I am not that tech savvy?
If it is - where can I go and rename it so it shows my MacBook name?
Anyway, I am going to tell you what I did if this is relevant for anything you were wondering about. Otherwise you don't have to read the statements below.
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Bob said:
Power off the entire network....all devices....in any order that you wish when you go to bed tonight.
In the morning, power up the modem first and let it run a minute by itself
Power up the next device connected to the modem the same way
Power up the next, etc.
Keep powering up devices one at a time until the network is back up
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I did that this morning.
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John said:
The TC will retain the client's IP address until its DHCP lease expires, or you cycle its power.
If you had a visitor with an iPhone or iPad or iPod Touch the TC will remember its IP address long after he's gone. Don't forget the guest network - if you enabled it, it's open.
"Ping" that address using Terminal - if the client is no longer present you will get 100% packet loss so that was likely the source of this mystery. On the other hand if you get returns the times shown may be useful.
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I have AU 6.1 and it shows on the TC in the Internet Tab option for "Renew DHCP Lease", but I haven't touched it yet, as I don't know what exactly to do. However, I did cycle power the modem.
And yes, I had visitor a while back (approx. 4 weeks ago) - he has an iPad and and an iPhone too. Both were not on my WiFi though. They were on my Wi-Fi before that - around 8 weeks ago. But at that time I had a different ISP. I don't know if that's important to be mentioned.
Guest Newtwork is disabled.
John, I don't know how to "ping" any address in Terminal. Which address are you referring to?
Bob is right - iPhones and iPads come and go as wireless clients depending on sleep/power off or when they are not on any Wi-Fi but on their celular network.
John, Yes, all screen shots are from my MacBook 13" AL, late 2008 (yes, I know it is old) running on Mac Lion v.10.7.5.