Color page is quite different but also in many ways the same to edit page, people don't often realize that. Did you know you have up to four playheads in the color page? Should we request the same in the edit page?
Look, I got four playheads controlling four clips in at least four different ways.

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I think people asked for this before. Technically it works the same way as edit page. People just don't realize it. If in the color page, you switch the node tree from clips to timeline, the viewer in color page is the same as edit page. As is the mini timeline. Moving between color page and edit page also honors the location of the selected clip. its just that people don't realize that timeline viewer is usually a viewer of the timeline on the edit page, with all the clips on the timeline. And when you click on a clip in the timeline the location is honored in the equivalent timeline on the color page. They are the same.
When you click on each clip in the thumbnail, you basically same type of timeline as if you loaded a clip into source monitor view on the edit page. You can confirm this if you double click on the clip on the edit page and load it into source viewer. Will the playhead move to the beginning each time? But viewer in color page is much more powerful and versatile its its own thing. There are no cut tools to edit in the color page, its a different animal. I don't know what kind of work you do to rely on position of playhead between clips on the color page, but I don't think that is the intention.
Make a compound clip of everything on the timeline and go to edit page. Tell me if they are not the same thing and playhead does not same on the same position? Between edit page and color page. People don't understand that when they are clicking on thumbnails in the color page, they are working on not one track, but multi track. Every clip thumbnail is positioned next to each other, regardless if they are on first or last track in the edit page, because that is the way color page is meant to be used for speed and task it is designed for. There quite a few important reasons for this. One is grading in groups and copy pasting grades that is not something edit page needs to do. The other reason is moving from one clip to the next, often short cuts, and you can just move to the next shot and next shot covering the whole timeline and continue grading or use clips to grade based on groups. Color page has no cutting the timeline tools. Its designed for something else and this method works quite well.
Trying to make it behave like edit page is like trying to color grade a feature film on the edit page. Why would you do that?
Color page can have versions of grades, and now we even have node stacks, process quite different than that of editing clips in edit or cut page. These are not accessible on the edit page, not to mention its further downstream the image processing chain. Like I said you can have up to four playheads and four clips in same monitor on multiple tracks and multiple node stacks and many more nodes. Have you ever check the number of different modes you can use to check your clips on the color page? Color page is not edit page, and that is a good thing. More options for all kinds of users. Great. But I think many users should first learn the reasons why things are the way they are before asking for something new. That's fair, would you agree?
P.S.
If you click between the clips on the color page and no other function to view them differently was performed, than keeping the playhead where it was last would be ok I guess. Interestingly, the other day someone on the edit page requested the reverse. They wanted the play head to reset to the start of the clip when they select the clip on the timeline.