Hi, @edwardandirwyn .
Great question! This is definitely a common issue, so you are not alone.
The issue is, when an item is only available for pick up, the other item in the order must also be available for pickup at the same location. If you have one location for pickup only, the products are not compatible as they are viewed by the system as available at separate locations. You also run into the issue that one is available to ship, while the other is not, thus you have no compatible shipping options.
The best solution for this would be to delete this new location you created, and restock your products at the same location as the rest of your inventory. Then, you will change your pick up location back to this location.
Next, you will create a new shipping profile for all of your local pick up products. However, the difference is, you will not create any shipping rates in this profile. What this will do, is trigger the system to provide a pick up option only, as there are no shipping rates. Because these products are also stocked at the same location as your ship-able products, the customers will be able to check out with a pick up option. Keep in mind, however, that they will not be able to select shipping. Pick up will be the only option.
If you would like the customer to be able to pick up on product, and ship the other, you will need to use an app. The app I always recommend, as it’s the most robust option, is Advanced Shipping Rules. This all allows you to create unlimited filters and rules for your products and locations for any shipping requirement.
In the meantime, I would love to learn more about your business! Do you have a storefront? Or are these products available to pick up at your home?