If I understand properly, you wanted to use the color picker for color stops of Gradient Tool.
I place here a solution because it looks very useful and not straightforward considering many questions in Google (and my 10 minutes self-updating research).
The workflow is:
Open Gradient tool panel
Window –> Gradient
or press Command/Control+F9, if you're on MacBook Pro etc you should use Fn+Command/Control+F9
Select the object with applied gradient
Click once on the color stop you want to change

Click on the Eyedropper tool or press I
Press Shift+Click on the color of one of the objects you want to apply to the color stop.
You're done.
Answer from Ilan on Stack ExchangeHow to change gradient Color in Illustrator? - Content - SitePoint Forums | Web Development & Design Community
How to use the color picker along the gradient tool in illustrator? - Graphic Design Stack Exchange
Is it possible to edit a Gradient Swatch in Illustrator's UI? - Graphic Design Stack Exchange
How would I change a selection’s colors to a gradient?
Select the object and then use the gradient tool - which has options for rotation of gradient, colour of gradients, opacity, etc.
https://helpx.adobe.com/ca/illustrator/using/gradients.html
More on reddit.comVideos
If I understand properly, you wanted to use the color picker for color stops of Gradient Tool.
I place here a solution because it looks very useful and not straightforward considering many questions in Google (and my 10 minutes self-updating research).
The workflow is:
Open Gradient tool panel
Window –> Gradient
or press Command/Control+F9, if you're on MacBook Pro etc you should use Fn+Command/Control+F9
Select the object with applied gradient
Click once on the color stop you want to change

Click on the Eyedropper tool or press I
Press Shift+Click on the color of one of the objects you want to apply to the color stop.
You're done.
If you must, you can use the eye-dropper tool to load a color in the color well.
It's better to get in the habit of using swatches. Then you know you have right values throughout. For gradients you simply drag a swatch onto the swatch tab on the gradient slider.
Illustrator has a big leg up on Photoshop with global colors. If you check this option, you can change the color throughout your document by simply editing the swatch.
Let’s say I have a flag and I want it to be the original color on one half and fade into an entirely different color on the opposite half, how would I go about this? Could I make the color change diagonal? Straight up and down? Wavy?
Forgive me, I’m so very new to Illustrator, I’m doing my best to learn, but keep finding small things that I don’t know how to do, and I’m not sure how exactly to word them to find the right tutorials to follow.
Select the object and then use the gradient tool - which has options for rotation of gradient, colour of gradients, opacity, etc.
https://helpx.adobe.com/ca/illustrator/using/gradients.html
I really enjoyed Dan Scott's walk-through on the gradient tool in his Illustrator beginner tutorial. 2:07:04 is where that section starts in the video. The whole video is worth the watch, honestly. It's broken up into sessions, which is great.
https://design.tutsplus.com/adobe-illustrator-for-beginners--ytc-5c
Hi there,
Currently working on a large .ai file for a camo pattern. There are multiple layers of different shapes and colours. Two of these layers have gradients across the shapes.
The gradient colours are the same across all shapes, however the direction is different between each. There is something like a hundred shapes in each layer…can I select all and change the colours without affecting the directions of the gradients somehow?