GP Header does not work on Woo shop Page.

Thats correct, you need to assign one in the Global Locations > Archives > Products.
Same goes for any archive pages.

No you can add headers to the woo category pages from the Layout box in edit page. But not possible on shop page.

My bad, yes Tom added the function for Woo categories but you're general blog and shop page has to be done via global locations.

There is another problem here.

If I add a custom header to the Woo shop in global settings it appears when I do a search that returns products.
However it does not appear when you do a search and the return is no products found.

And I have checked and that file path and it is the same product-archive.php template file in both instances.

How can we fix this?

I generally add a Page Header to the Search Results in Global Locations. My experience is search results don't normally grab the shop page header.

There is an issue here. A bug that need some attention unless I am getting things wrong. Which is more often than not....

I need to add a header to my Woo search results.

Sure if I set that header in the Global Search drop down it will appear in my woo searches.

But the problem is it will also appear in my Blog searches...which is not right.

The Search Global header settings currently adds the selected header to both the woo archive-product.php template and to the WP search.php template.

The header I want to use for my woo searches is not suitable to appear at the top of my wp searches.

How can I set a header at the top of my woo searches only?

Can you check with WooCommerce to see if there is a specific template tag for WooCommerce search results page we can use? I tried to look around but not seeing it.

Then we can use this filter:
https://docs.generatepress.com/article/generate_page_header_id/

Let us know :)

The search results page is the archive-product.php template?

if ( is_shop() ) {

or

if ( is_search() ) {

Definitely doesn't hurt to test. Or try a combination of both?

Or maybe something like is_woocommece() && is_search()?

Worth checking with their support.