Can a native English speaker explain what "I saw a shiny thing" means?

It's a metaphor. He was comparing seeing the woman to seeing an attractive or valuable object like a coin on the ground or a jewel.

They see a good looking attractive woman and spy on them. Their low IQ vanishes completely and all the blood rushes to their pants.

They are like a toddler in a toy store and want the shiniest thing.

The police officer is saying that he is so brain damaged or otherwise incapable of self control, rational thought, and restraint, that an attractive woman existing in his presence caused him to immediately commit many crimes to see her again.

Pay close attention to how he insists that she was coming on to him. He genuinely believes that. He lives in a fake reality that he adjusts in whatever way will make him happiest because he has spent so long in a system that has zero repercussions or accountability.

He probably shouldn't be allowed to own a gun.

Men like this know they are doing bad things. They don't care. There are no repercussions. They do not feel bad about doing these bad things.

See also: https://www.bwss.org/abusive-men-describe-the-benefits-of-vi...

Basically, these people just choose to not care about other people. They know they are hurting someone. But minor personal convenience is more important to them than not hurting another person.