How long can a cop follow you for an expired tag?

Question Details: I drove by a cop who apparently has a plate reader. My tag was expired due to financial issues. I watched the cop for half a mile without him ever moving or even appearing to move. After driving for about a mile And on a separate road as when I passed the cop I see him speeding to catch up to me. I was literally right in front of my house when he pulled me over for the expired tag. I didn't break any other laws, so I was wondering if this was a legal stop. I don't see why he didn't pull me over when he first saw me. Why did he wait for me to get over a mile away from him only to catch up to me and stop me?

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